Actually, United doesn't pay much attention to weight. The MAXIMUM per piece is 70 POUNDS... they only weigh bags if they seem close to it.
Star Silver/Gold members are allowed 3 checked pieces, while standard luggage is 2. If you are moving away from college, you //can// check 2 of the large plastic tubs w/ all your stuff in it
For carry-on... they don't weigh them or even look at them... but keep it below 45 pounds.
Extra luggage is $75 per I believe (I've never had to pay, thank god).... sometimes they charge, sometimes they don't.