fill out
fill out {v.}
1. To put in what is missing; complete; finish; {especially}, to complete (a printed application blank or other form) by writing the missing facts in the blank spaces; to write down facts which are asked for in (a report or application.)
After Tom passed his driving test he filled out an application for his driver's license.
The policeman filled out a report of the accident.
2. To become heavier and fatter; gain weight.
When Bill was nineteen he began to fill out.
The girl was pale and thin after her sickness, but in a few months she filled out.
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Source: A Dictionary of American Idioms