You could take the seat over to Atlee Dodge, and see if Steve Kracke can weld it. Upholstery would have to be removed/replaced.
That is ONE of the weak points of Cessna adjustable seats. As noted earlier, rear seat passengers are really wont to grab the top of the seat back and haul their lard butts out of those back seats......and do this kind of damage. This is especially so in tailwheel airplanes, where it's an uphill struggle to get out of the rear seats. Usually the damage is to the roll pins, though, not the frame. I suspect this seat was previously cracked and you just put it over the edge, so to speak. When I was flying 185s for a living, this was something that I lectured back seaters on. The other REALLY damaging behaviour is when a front seater gets in, then pushes real hard with his/her feet and against the top of the seat back to adjust their undies for the upcoming flight. There's a LOT of leverage in that process. That was the quickest way to get yelled at by me in one of these things.
Which is to say, I'd also check the other seat while you're at it, could be similar damage that just hasn't completely failed on that seat. In meantime, if you want to fly, switch the front seats. AFTER you check that one for damage, of course.
And, consider what would happen if this were to occur during the takeoff run, for example.....not quite as bad as having the whole seat slide back on the tracks, but.....not good in any case.
If you damage the upholstery in your search for damage, there's an outfit in Anchorage that advertises on here that can likely fix you up.
Good luck, and welcome to old airplane ownership.
MTV