GridLayout (not GridView) how to stretch all children evenly

Starting in API 21 the notion of weight was added to GridLayout. To support older android devices, you can use the GridLayout from the v7 support library.

The following XML gives an example of how you can use weights to fill the screen width.

<?xml version="1.0" encoding="utf-8"?>
<android.support.v7.widget.GridLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:grid="http://schemas.android.com/apk/res-auto"

    android:id="@+id/choice_grid"
    android:layout_width="fill_parent"
    android:layout_height="wrap_content"
    android:layout_centerHorizontal="true"
    android:padding="4dp"

    grid:alignmentMode="alignBounds"
    grid:columnCount="2"
    grid:rowOrderPreserved="false"
    grid:useDefaultMargins="true">

    <TextView
        android:layout_width="0dp"
        android:layout_height="100dp"
        grid:layout_columnWeight="1"
        grid:layout_gravity="fill_horizontal"
        android:gravity="center"
        android:background="#FF33B5E5"
        android:text="Tile1" />

    <TextView
        android:layout_width="0dp"
        android:layout_height="100dp"
        grid:layout_columnWeight="1"
        grid:layout_gravity="fill_horizontal"
        android:gravity="center"
        android:background="#FF33B5E5"
        android:text="Tile2" />

    <TextView
        android:layout_width="0dp"
        android:layout_height="100dp"
        grid:layout_columnWeight="1"
        grid:layout_gravity="fill_horizontal"
        android:gravity="center"
        android:background="#FF33B5E5"
        android:text="Tile3" />

    <TextView
        android:layout_width="0dp"
        android:layout_height="100dp"
        grid:layout_columnWeight="1"
        grid:layout_gravity="fill_horizontal"
        android:gravity="center"
        android:background="#FF33B5E5"
        android:text="Tile4" />

</android.support.v7.widget.GridLayout>

Starting in API 21 without v7 support library with ScrollView:

XML:

<?xml version="1.0" encoding="utf-8"?>
<ScrollView
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    >

    <GridLayout
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            android:columnCount="2"
            >

        <TextView
            android:layout_width="0dp"
            android:layout_height="100dp"
            android:layout_columnWeight="1"
            android:gravity="center"
            android:layout_gravity="fill_horizontal"
            android:background="@color/colorAccent"
            android:text="Tile1" />

        <TextView
            android:layout_width="0dp"
            android:layout_height="100dp"
            android:layout_columnWeight="1"
            android:gravity="center"
            android:layout_gravity="fill_horizontal"
            android:background="@color/colorPrimaryDark"
            android:text="Tile2" />

        <TextView
            android:layout_width="0dp"
            android:layout_height="100dp"
            android:layout_columnWeight="1"
            android:gravity="center"
            android:layout_gravity="fill_horizontal"
            android:background="@color/colorPrimary"
            android:text="Tile3" />

        <TextView
            android:layout_width="0dp"
            android:layout_height="100dp"
            android:layout_columnWeight="1"
            android:gravity="center"
            android:layout_gravity="fill_horizontal"
            android:background="@color/colorAccent"
            android:text="Tile4" />

    </GridLayout>
</ScrollView>

UPDATE: Weights are supported as of API 21. See PaulT's answer for more details.

There are limitations when using the GridLayout, the following quote is taken from the documentation.

"GridLayout does not provide support for the principle of weight, as defined in weight. In general, it is not therefore possible to configure a GridLayout to distribute excess space in non-trivial proportions between multiple rows or columns ... For complete control over excess space distribution in a row or column; use a LinearLayout subview to hold the components in the associated cell group."

Here is a small example that uses LinearLayout subviews. (I used Space Views that takes up unused area and pushes the buttons into desired position.)

<GridLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:columnCount="1"
>
    <TextView
        android:text="2x2 button grid"
        android:textSize="32dip"
        android:layout_gravity="center_horizontal" />

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content" android:orientation="horizontal">
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
        <Button
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:text="Button 1" />
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
        <Button
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_gravity="start"
            android:text="Button 2" />
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
    </LinearLayout>

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:orientation="horizontal"
    >
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
        <Button
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:text="Button 3" />
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
        <Button
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_gravity="start"
            android:text="Button 4" />
        <Space
            android:layout_width="wrap_content"
            android:layout_height="match_parent"
            android:layout_weight="1" />
    </LinearLayout>
</GridLayout>

Appcompat21 GridLayout has the column and row weights which can be used like below to evenly create each grid item in the gridlayout like the image above.

<android.support.v7.widget.GridLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:grid="http://schemas.android.com/apk/res-auto"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:layout_centerHorizontal="true"
    grid:alignmentMode="alignBounds"
    grid:columnCount="4" >

    <Button android:layout_width="0dp"
        style="?buttonStyle"
        android:layout_height="0dp"
        android:text="-1"
        grid:layout_columnWeight="1"
        grid:layout_rowWeight="1"
        grid:layout_gravity="fill" />
    ...
</<android.support.v7.widget.GridLayout>