This is weird. Good weird, definitely improved my day. But, still weird.
The extra time he gets is interesting... If this has been happening about weekly since he was twelve, and it is now four years later, he is getting 9-day weeks. Which is roughly +1/4 or about +28%. That would mean, if the extra time in the other world ages him, he's now about 17yrs old, not 16yrs - you can bet his school records don't reflect that.
Survivalist Xander, ready for the disappearance of civilization at a moment's notice...
I wonder if anyone has thought to teach him how to read the stars, or got him to bring back a series of good photos of them? Assuming this is the same as Earth's solar system, the position of the stars and the planets is a clock, and it should be possible to tell if time is passing evenly in the other world, or if he might be doing something like mini (2 day) time jumps, between worlds, as well.
I guess this is "The man who walked around the horses", Bathhurst, who is one example of a mysterious disappearance. Colin Wilson wrote about a number of such weird stuff in "The Occult":http://en.wikipedia.org/wiki/The_Occult:_A_History
I liked that Wilson listed weird appearances, as well; two children with green skin who appeared in (medieval?) Wales, and spoke no known language, was I think one of them.
Lots of stuff in science fiction, about world hopping, of course.
The way the Mayor has helped Xander is interesting. A 'bag of holding' or such, but, rather understated. If world hopping (and return!) is a rare talent, even near the Hellmouth, you could see why he'd take an interest. Having someone who could get him out of Sunnydale might be very useful to him, even if he couldn't figure out how to duplicate the ability using magic. If nothing else, a couple of extra days to work on something, which is portable, at a critical time, could be incredibly useful. And, if nothing else, he's taking a civic interest in one of his constituents. And, maybe providing 'survival holidays' for a few of his associates.
Nice to have someone, really early on, who might almost make the weirdness in Buffy's life look 'normal'... The empathy between the couple is interesting. Giles, of course, wont approve, but you can bet he'll try and research Xander's ability.
A few rough calculations might suggest this Buffy is lifting maybe 5 tons, then throwing that 30 feet. If that scales she could throw a large human maybe 150 feet? That is an impressively strong Buffy...
I'm guessing Xander's arrival point avoids anywhere that would prevent short-term survival, like the middle of the ocean, or close enough to a pole, or too high to easily breathe, say, on Mt. Everest. Probably avoids underground spaces, as well.
I'll admit to being curious as to whether it's the same world Xander goes to, each time, and if he's ever been close enough to where he visited previously to tell if he'd left any signs. Earth is a big place - unless he got lucky he might never be able to tell, one way or another. It might even be a small number, say less than a dozen, and no one might ever know. Unless, maybe, the Mayor is cross-world skrying him, and has got some way of identifying, or distinguishing, the worlds he skrys. Or, maybe getting Xander to directly or indirectly leave a marker talisman behind.
For real fun, I guess the world(s) he visits might be tidying-up after he leaves, erasing anything out-of-place. Maybe any people he left behind, like Harmony, particularly being a Hellmouth resident, might survive that. Maybe Harmony has a strange Hellmouth-y talent, apart from becoming a nicer person by being vampirised? [grin]
That even discounts other world hoppers, "GURPS Infinite Worlds" stuff, and dimensional travel police. Is this place outside the reach of the Powers That Be, and the Senior Partners? The powers that can be got by calling on beings like Hecate, Janus or even (Roman) ones like Terminus? Beyond the reach of vengeance demons?
So many possibilities...
I guess the odds of you continuing this aren't very high, but, I think it's fun.