Fetching details from the dictionary...

to put clothes on (someone); to dress; to clothe
to cover; to coat; to plate; to gild; to veneer
to pin (e.g. a crime on someone); to lay (blame); to charge (with an offence); to give (a bad name); to remind someone of (their indebtedness)
寒いので子供に毛布を被せてあげることにしたよ。
It's cold, so I decided to put a blanket over the child.
帽子を被せると日焼け防止になるから忘れずにね。
Putting on a hat prevents sunburn, so don't forget.
赤ちゃんに上着を被せた。
I put a jacket on the baby.