The bottom hinge is fine but the top hinge is hanging off despite me regularly tightening the screws. The door is a heavy interior one and I think the screws have nothing to grip so I'm assuming I need to take the hinge off and fill it or resite it or something. Help.

Try a toothpick in the hole, break flush and insert screw. One at a time.

Another alternative is Plastic Wood. You can find it in most hardware stores.

Plastic anchor. Drill out existing hole slightly if necessary.

Try using Longer screws

All may work to limited success but I'd go with the longer screws. Get a set of screws long enough to reach through the door frame and get into the framing of the door opening, maybe a 3" screw.

And if you hit concrete, maybe use Long TapCons.

Is the problem on the door jamb or the door? If the jamb use longer screws. If the door and it's a solid wood door use longer screws. If it's a hollow core door use plastic anchors and larger longer screws. Tooth picks and wood glue will work also.

Since this is a heavy door I think long screws will hold the weight. Tooth picks, glue and plastic anchors ask the jam to carry the full load but the stud frame will better carry a heavy load, use 3+" screws

Most interior hinges have 3 places for screws. As mention a long screw through the hinge (http://ezhangdoor.wordpress.com/page/3/) and jamb into the wall framing will hold the heavy door. However, this will only work on the center screw hole. On the other two screw holes, normally they are lined up with where the drywall is, so you won't hit any framing with those two holes. Use a glue and a golf tee to fill those holes. This will fix the stripped screw holes. (http://www.ezhangdoor.com/how-to-fix-a-stripped-screw-hole)

EZHangDoor & ballengerb1 are correct.
Just besure not to over tighten the 3" screw or you will pull your door out of wack & or damage your door casing.You can also align your door with the screw if the gap is out.
Hope this helps