To check OUT someone, or checking someone OUT, is used to mean appraising the person's attractiveness, figuring out how likely the two of you would get along well, etc. E.g., "Hey--she's totally checking you out, dude!"

I guess checking OUT ON someone would be a figurative expression indicating that someone is distracted, daydreaming, "zoned out," "a thousand miles away," etc., etc.
E.g., "He's not even listening anymore. He checked out (on us) a while ago." However, I'm not sure if this wording is used commonly or not.

To check UP ON (but not "upon") someone is to investigate that person's progress, status, etc. E.g., "My mom kept checking up on me to see if I was really working on my homework or not." May have a negative connotation, if the speaker feels the other person is being nagging, intrusive, controlling, etc.

Simply to check ON someone means to ascertain that person's wellbeing; e.g. "You OK? You said you weren't feeling well, so I just thought I'd check on you."

To check IN WITH someone means to provide that person with a status update of your condition. E.g., "Hey, once I get to the airport, I'll call you to check in (with you), OK?"

To check IN ON someone... I'm not sure whether I've heard that expression or not. :-/ I suppose it would be similar to "checking up on," but without the negative connotation?

.....And then of course there is the wording applied specifically to materials obtained at a library: "checking out" (borrowing) and "checking in" (returning) books or other media.

(This was going to be shorter, but I kept thinking of more prepositions! >~<)

I agree with the above. I think for "check in on" you would use it when you're checking the status of someone else, such as someone in the hospital. "I went to the hospital to check in on my mother." But I don't think it's really commonly used.