It doesn't look like you have posted the entire layout XML. I suspect you have padding or set a margin for one of the elements enclosing @id/bannerLayout. Remove the padding/margin (nb it might be in a style you have applied).
I also suggest you alter the layout_width and layout_eights as follows:
<LinearLayout
android:id="@+id/bannerLayout"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_alignParentBottom="true"
android:layout_alignParentLeft="true"
android:layout_alignParentRight="true"
android:layout_below="@+id/button2" >
<com.google.android.gms.ads.AdView
android:id="@+id/adView"
android:layout_width="match_parent"
android:layout_height="wrap_content"
ads:adSize="BANNER"
ads:adUnitId="@string/adMobIDSmall" />
</LinearLayout>