1. To watch another person's child or children. In this usage, the child is listed after "for." Julia will babysit for the kids on Saturday.
2. To help another person by watching their child. In this usage, the person being helped is listed after "for," and a noun can be used between "babysit" and "for." Can you babysit for us tonight? Dave's company is having a work event that we have to go to. I got one of the neighbors to babysit Charlotte for me so I could come to the party.
babysit for someoneand babysit (with) someone
1. to attend and care for a child for a period of time. I'm looking for someone to babysit for my cousin. Will you babysit with my cousin?
2. to attend and care for a child for someone for a short period of time. Would you mind babysitting Roger for me for a few minutes? Sure, I will babysit for you.