As already said, yours could easily have stretched since new, so tightening up a bit is a good idea. But you definitely don't want to keep it too tight for too long either for the reasons stated.
You should at least try to get it snug before it glazes up the pulley too much though.
Standard alternator cases have the adjustable, threaded hole surrounded by a square boss. You can either use a wrench of some kind to grip this and push/pull while tightening the bolt. Or you can even use one of those j-hook looking scimitar thingies to grip it and then put your 1/2" drive ratchet in to leverage things.
Whichever is more convenient in your particular installation.
Or better yet if you can fit it, is one of the turnbuckle style setups that put outward pressure on the alt. Again though, just don't try to mash it out or you'll be regretting it later.
If your setup allows, a dual-groove pulley is a good answer. If you can find one that's a tiny bit larger diameter and has deep grooves, so much the better.
But 3G's are why many of us go with serpentine in the first place.
Good luck.
Paul