oh, don't tweeze it... get yourself to a good electrologist asap. it does work - its not an instant fix - but it does work. the best way to do electrology is find a place with a good reputation (not just someone in a back room with a machine). and here's the bad part: it has to hurt. if its going to be at all effective, they have to turn the current up very high - and it has to hurt. ANYONE who tells you anything different is trying to rip you off by drawing out your treatments into forever. the current must be so high it hurts bad, and leaves a slight red dot of blood behind, but NOT a scar. when they pull the hair out - it should almost fall out and there should be no "plucking" sensation. then the hair is gone until you notice it growing back again and then you go back for the next treatment (u can shave in between treatments, but you can't pluck or tweeze - plucking the hair only strengthens the follicle and makes the treatment time much longer). treatments should be every other week or even every week in the beginning. they only cost around $20-$30 for a half hour though - which is plenty - those electrologists are fast and can remove a lot of hair very quickly.
but here's the good part - there's a way to stop the pain. what you do, is you see a gynecologist - explain to him/her that you are having this facial hair-growth and that you are going to go to an electrologist. then tell your gyno to give you a prescription for EMLA cream - apply the cream 1hr before the electrolysis and voila! no more pain. neat huh?
that's what i do. i had almost a full beard and its really almost gone and the remaining hairs only grow back once every 3 months or so and are very light and fine. good luck.