Android Webview app won’t let video player go full screen

You need to implement showCustomView & hideCustomView method of WebChromeClient, also You need android:hardwareAccelerated="true" in your AndroidManifest File.
I am posting my sample project here.
What i have done is kept one Framelayout(customContainer) in my main.xml, and adding view received in showCustomView here, and removing it in onHide. Also hiding/showing webview accordingly. Below code works perfectly on device.

AndroidManifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
          package="com.example.webview"
          android:versionCode="1"
          android:versionName="1.0">
    <uses-sdk android:minSdkVersion="8"/>
    <uses-permission android:name="android.permission.INTERNET"/>
    <application android:label="@string/app_name" android:icon="@drawable/ic_launcher"
            android:hardwareAccelerated="true">
        <activity android:name="MyActivity"
                  android:configChanges="orientation|keyboardHidden"
                  android:hardwareAccelerated="true"
                  android:label="@string/app_name">
            <intent-filter>
                <action android:name="android.intent.action.MAIN"/>
                <category android:name="android.intent.category.LAUNCHER"/>
            </intent-filter>
        </activity>
    </application>
</manifest>

main.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
              android:orientation="vertical"
              android:layout_width="fill_parent"
              android:layout_height="fill_parent"
        >
    <WebView
            android:layout_width="fill_parent"
            android:layout_height="fill_parent"
            android:id="@+id/webView"
            android:layout_gravity="center"
            />
    <FrameLayout
            android:id="@+id/customViewContainer"
            android:layout_width="fill_parent"
            android:layout_height="fill_parent"
            android:visibility="gone"
            />
</LinearLayout>

video_progress.xml

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
              android:id="@+id/progress_indicator"
              android:orientation="vertical"
              android:layout_centerInParent="true"
              android:layout_width="fill_parent"
              android:layout_height="fill_parent">

    <ProgressBar android:id="@android:id/progress"
                 style="?android:attr/progressBarStyleLarge"
                 android:layout_gravity="center"
                 android:layout_width="wrap_content"
                 android:layout_height="wrap_content"/>

    <TextView android:paddingTop="5dip"
              android:layout_width="wrap_content"
              android:layout_height="wrap_content"
              android:layout_gravity="center"
              android:text="loading"
              android:textSize="14sp"
              android:textColor="?android:attr/textColorPrimary"/>
</LinearLayout>

MyActivity.java

package com.example.webview;

import android.app.Activity;
import android.graphics.Bitmap;
import android.os.Bundle;
import android.view.KeyEvent;
import android.view.LayoutInflater;
import android.view.View;
import android.webkit.WebChromeClient;
import android.webkit.WebView;
import android.webkit.WebViewClient;
import android.widget.FrameLayout;

public class MyActivity extends Activity {
    private WebView webView;
    private FrameLayout customViewContainer;
    private WebChromeClient.CustomViewCallback customViewCallback;
    private View mCustomView;
    private myWebChromeClient mWebChromeClient;
    private myWebViewClient mWebViewClient;

    /**
     * Called when the activity is first created.
     */
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
        customViewContainer = (FrameLayout) findViewById(R.id.customViewContainer);
        webView = (WebView) findViewById(R.id.webView);

        mWebViewClient = new myWebViewClient();
        webView.setWebViewClient(mWebViewClient);

        mWebChromeClient = new myWebChromeClient();
        webView.setWebChromeClient(mWebChromeClient);
        webView.getSettings().setJavaScriptEnabled(true);
        webView.getSettings().setAppCacheEnabled(true);
        webView.getSettings().setBuiltInZoomControls(true);
        webView.getSettings().setSaveFormData(true);
        webView.loadUrl("http://m.youtube.com");
    }

    public boolean inCustomView() {
        return (mCustomView != null);
    }

    public void hideCustomView() {
        mWebChromeClient.onHideCustomView();
    }

    @Override
    protected void onPause() {
        super.onPause();    //To change body of overridden methods use File | Settings | File Templates.
        webView.onPause();
    }

    @Override
    protected void onResume() {
        super.onResume();    //To change body of overridden methods use File | Settings | File Templates.
        webView.onResume();
    }

    @Override
    protected void onStop() {
        super.onStop();    //To change body of overridden methods use File | Settings | File Templates.
        if (inCustomView()) {
            hideCustomView();
        }
    }

    @Override
    public boolean onKeyDown(int keyCode, KeyEvent event) {
        if (keyCode == KeyEvent.KEYCODE_BACK) {

            if (inCustomView()) {
                hideCustomView();
                return true;
            }

            if ((mCustomView == null) && webView.canGoBack()) {
                webView.goBack();
                return true;
            }
        }
        return super.onKeyDown(keyCode, event);
    }

    class myWebChromeClient extends WebChromeClient {
        private Bitmap mDefaultVideoPoster;
        private View mVideoProgressView;

        @Override
        public void onShowCustomView(View view, int requestedOrientation, CustomViewCallback callback) {
           onShowCustomView(view, callback);    //To change body of overridden methods use File | Settings | File Templates.
        }

        @Override
        public void onShowCustomView(View view,CustomViewCallback callback) {

            // if a view already exists then immediately terminate the new one
            if (mCustomView != null) {
                callback.onCustomViewHidden();
                return;
            }
            mCustomView = view;
            webView.setVisibility(View.GONE);
            customViewContainer.setVisibility(View.VISIBLE);
            customViewContainer.addView(view);
            customViewCallback = callback;
        }

        @Override
        public View getVideoLoadingProgressView() {

            if (mVideoProgressView == null) {
                LayoutInflater inflater = LayoutInflater.from(MyActivity.this);
                mVideoProgressView = inflater.inflate(R.layout.video_progress, null);
            }
            return mVideoProgressView;
        }

        @Override
        public void onHideCustomView() {
            super.onHideCustomView();    //To change body of overridden methods use File | Settings | File Templates.
            if (mCustomView == null)
                return;

            webView.setVisibility(View.VISIBLE);
            customViewContainer.setVisibility(View.GONE);

            // Hide the custom view.
            mCustomView.setVisibility(View.GONE);

            // Remove the custom view from its container.
            customViewContainer.removeView(mCustomView);
            customViewCallback.onCustomViewHidden();

            mCustomView = null;
        }
    }

    class myWebViewClient extends WebViewClient {
        @Override
        public boolean shouldOverrideUrlLoading(WebView view, String url) {
            return super.shouldOverrideUrlLoading(view, url);    //To change body of overridden methods use File | Settings | File Templates.
        }
    }

}

You can clone sample project from here..