Final answer:
The layout_weight attribute in a linear layout determines the allocation of space to an Android widget, with its value dictating how the remaining space is distributed among weighted elements.
Step-by-step explanation:
In a linear layout for Android applications, the layout_weight attribute determines how much space is allocated to a widget. The layout_weight is used to specify how much of the remaining available space in the layout should be allocated to the widget, after all the elements have been measured. If more than one widget has a layout_weight specified, the space will be distributed among these widgets based on their weight relative to the sum of weights of all elements in the linear layout.