Translation:Are you free on the weekend?
Americans, at least the Middle Atlantic variety, tend to use "this weekend" (specific) and "weekends" (in general) adverbially without any preposition. We tend not to say "at the weekend" (which sounds British to me) but we do say "for the/this/that weekend" and "on weekends." Generally it isn't good to be too prescriptive about prepositions because usage varies, particularly between British and American speakers.
In this sentence, "hima" means "free" in the sense that you don't have any plans. Sometimes, when a Japanese person says "hima", it can mean "I don't have anything to do so I'm bored". This connotation of being "bored" is contextual and not the best definition, but it is possible.