have a lot on
To have several things scheduled; to have multiple things happening at a particular time. Unfortunately, I have a lot on this weekend, so I can't hang out.
have anything on
To have plans scheduled; to have something happening at a particular time. Do you have anything on this weekend? If not, do you want to hang out?
not have a lot on
To have very few or no plans scheduled; to have not much happening at a particular time. I don't have a lot on this weekend—do you want to hang out?
not have anything on
1. To have no plans scheduled; to have nothing happening at a particular time. I don't have anything on this weekend, do you want to hang out?
2. To have no clothes on; to be naked. One moment, please. I'm just out of the shower and don't have anything on!