The guys at our uni gym are quite nice, besides the usual guy-gossiping and hovering around doing nothing (but they usually are willing to share or give up their bars/spots if they aren't doing anything productive, when I ask them). I've had some guys staring at my deadlifting and squatting, but nothing too bad. Besides me and my friend, I've only seen a few girls doing biceps curls, goblet squats and stuff like that with light dumbbells.
I think it's just a question of developing a proper attitude; you have the right to be there using the weights or other machinery, to do your workout and then get out. If they start making stupid comments, you should just ignore them, stare at them scornfully as if they were dog ****, or pay back in kind by criticising their lifting (especially if they're the kind that can curl a lot, but couldn't deadlift to save their lives). No one's been stupid enough to insult me, so I haven't had a chance to rip into anyone yet
It helps when you're confident in what you do; even though I'm quite a confident person, I always hesitate a bit before trying a new lift (for example I only tried benching for the first time, when my friend was there to spot and the gym was quite empty). But otherwise I come in, mind my own business, work through my lifts and then leave.
And fran, if you can take some of the weights with you to another area, do that, but don't bother with the swiss ball. For example just work on goblet squats and modified deadlifts, shoulder press etc. with the dumbbell until you feel comfortable enough to go back to the proper weights area and work with an empty barbell.
Also probably found myself a training partner. He used to be quite big apparently, but he's been cutting down, and recently joined our boxing gym for conditioning, while still doing strength training at our uni gym. Can now maybe try to get my squats heavier, since he can spot for me (the other friend mentioned before is way too small to spot for heavy stuff).