Android :: Android EditText Not Take Up Remaining Space

In my Android app, I have a tabbed Activity. In one of the tabs I have two TextViews and two EditTexts. The first EditText is only one line, and that's fine. However, I want the other EditText, android:id="@+id/paste_code", to take up the remaining space, but no matter what I do to it, it will only show one line. I don't want to manually set the number of lines, since the number that would fit on the screen differs based on your device.

Here's the relevant code. It's nested inside all the necessary components for a tabbed Activity.

<ScrollView
android:id="@+id/basicTab"
android:layout_width="fill_parent"
android:layout_height="fill_parent" >
<LinearLayout
android:orientation="vertical"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:layout_weight="1" >
<TextView
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:text="Paste title"
android:layout_weight="0" />
<EditText
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:hint="@string/paste_title_hint"
android:id="@+id/paste_title"
android:lines="1"
android:gravity="top|left"
android:layout_weight="0" />
<TextView
android:layout_width="fill_parent"
android:layout_height="wrap_content"
adroid:text="Paste text"
android:layout_weight="0" />
<EditText
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:hint="@string/paste_hint"
android:id="@+id/paste_code"
android:gravity="top|left"
android:layout_weight="1" />
</LinearLayout>
</ScrollView>