Set position / size of UI element as percentage of screen size

I think what you want is to set the android:layout_weight,

http://developer.android.com/resources/tutorials/views/hello-linearlayout.html

something like this (I'm just putting text views above and below as placeholders):

  <LinearLayout
    android:orientation="vertical"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    android:weightSum="1">
    <TextView
        android:layout_width="fill_parent"
        android:layout_height="0dp"
        android:layout_weight="68"/>
    <Gallery 
        android:id="@+id/gallery"
        android:layout_width="fill_parent"
        android:layout_height="0dp"

        android:layout_weight="16"
    />
    <TextView
        android:layout_width="fill_parent"
        android:layout_height="0dp"
        android:layout_weight="16"/>

  </LinearLayout>

Use the PercentRelativeLayout or PercentFrameLayout from the Percent Supoort Library

<android.support.percent.PercentFrameLayout
android:orientation="vertical"
android:layout_width="match_parent"
android:layout_height="match_parent">
     <TextView
          android:layout_width="match_parent"
          app:layout_heightPercent="68%"/>
     <Gallery 
          android:id="@+id/gallery"
          android:layout_width="match_parent"
          app:layout_heightPercent="16%"/>
     <TextView
          android:layout_width="fill_parent"
          android:layout_height="wrap_content"
          android:layout_width="match_parent"/>
</android.support.percent.PercentFrameLayout>

For TextView and it's descendants (e.g., Button) you can get the display size from the WindowManager and then set the TextView height to be some fraction of it:

Button btn = new Button (this);
android.view.Display display = ((android.view.WindowManager)getSystemService(Context.WINDOW_SERVICE)).getDefaultDisplay(); 
btn.setHeight((int)(display.getHeight()*0.68));

The above problem can also be solved using ConstraintLayout through Guidelines.

Below is the snippet.

<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent">

<android.support.constraint.Guideline
    android:id="@+id/upperGuideLine"
    android:layout_width="wrap_content"
    android:layout_height="wrap_content"
    android:orientation="horizontal"
    app:layout_constraintGuide_percent="0.68" />

<Gallery
    android:id="@+id/gallery"
    android:layout_width="0dp"
    android:layout_height="0dp"
    app:layout_constraintBottom_toTopOf="@+id/lowerGuideLine"
    app:layout_constraintEnd_toEndOf="parent"
    app:layout_constraintStart_toStartOf="parent"
    app:layout_constraintTop_toTopOf="@+id/upperGuideLine" />

<android.support.constraint.Guideline
    android:id="@+id/lowerGuideLine"
    android:layout_width="wrap_content"
    android:layout_height="wrap_content"
    android:orientation="horizontal"
    app:layout_constraintGuide_percent="0.84" />

</android.support.constraint.ConstraintLayout>