I do have a problem with my A/C cutting out at idle (and it cuts back in when I get going again), but I don't have a problem with too much slack - it's on pretty securely. I tried pushing on the belt and yanking on the tensioner pulley, but it stayed stuck.

If I move the pointer around, and try tightening the adjustment nut, the pointer WILL move - does that mean something's still working, or does the indicator work separately from the actual tensioning device?

(It's the original tensioner the car came with)