sit down on (someone or something)
1. To assume a sitting position on top of someone or something. There were no chairs left, so I had to sit down on the coffee table during the party. The woman said she was feeling dizzy, so I told her to sit down on the curb for a minute.
2. To place or set someone or something down on top of someone or something else. In this usage, a noun or pronoun is used between "sit" and "down." The father set the child down on chair in the corner of the room for a time-out. The coach came over and sat a big sandbag down on me to make it harder to do pushups.
sit down on something
to be seated on something. Please sit down on this chair and wait until you are called. I don't want to sit down on this hard bench.