What I'm looking for is a button right on the left with the textview centered in the remaining space:
|    text    button|
(| shows edge of screen)

What happens is this:
|text        button|

    <!-- This LL fills the screen width. -->
    <LinearLayout
	android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:orientation="horizontal" >
	<!-- This LL gets all the space to the left of the button due to weight 1 -->
	<LinearLayout
	    android:layout_width="0dip"
	    android:layout_height="match_parent"
	    android:layout_weight="1"
	    android:orientation="horizontal" >

	    <!-- This textview is always on the hard left -->
            <!-- no matter what layout_gravity is specified -->
	    <TextView
	        android:id="@+id/result_textview"
	        android:layout_width="wrap_content"
	        android:layout_height="wrap_content"
                <!-- center_vertical works as it should... -->
	        android:layout_gravity="center_horizontal|center_vertical"
	        android:text="testtest"
	        android:textAppearance="?android:attr/textAppearanceLarge" />

	</LinearLayout>

	<!-- This button is on the right edge of the screen as it should be -->
	<!-- due to default weight 0 -->
	<Button
	    android:layout_width="wrap_content"
	    android:layout_height="wrap_content"
	    android:text="@string/calculate_string"
	    android:onClick="myFunction" />
    </LinearLayout>