If it is a leak, the problem could be as simple as a bad O-ring but it could be more serious such as a damaged condenser, evaporator, or a bad compressor.
But, you mentioned the air out of the vents is weak. As Harley pointed out, it could just be a clogged cabin filter. That's an easy check on most cars ( many have them behind the glove box ).
$500. If it's really bad sometimes $1000. Yelp around for a reputable mechanic. Which is hard, but read the reviews besides only looking at the ratings. That may give you a slightly better deal, and plus the more expensive dealership might screw you anyway.
If you can handle very basic wrenching then you can get an AC recharge kit from an auto parts store. Make sure it's one with the fluorescent dye and get a black light too. You can check google, owner's manual or sometimes the Haynes manual for the location of the low pressure side refrigerant fill nozzle. Do NOT fill at the high pressure side refrigerant nozzle, won't work and it's very dangerous. Recharge your AC and check for leaks with the black light. If you're lucky then you won't find any leaks and you're done. If you do, then be prepared to pay a reputable mechanic a bunch to fix it.
If it has no leaks and a mechanic refills it for you, then it'll only be $100-$200.
Just go to Wal-Mart & get a can of freon. It may just need recharging. Just did mines. Been ice cold going on 3 months now ????
Below $2k
first check the cabin filter( pollen filter) isn't blocked
i have mitsubishi lancer GTS 2008 and the AC doesn't seems to be work, not totally but the cold air coming out from the AC is really really really weak. how much do you think it would cost me if i went to a dealership and fix my car?