Oh-- that's the fun part of trees. You don't know what it weighs until they cut it off,and if it weighs more than you can handle, you're along for the ride. Trees are one of the most dangerous jobs with a crane.
That said, you kind of learn about what a piece will weigh, just by looking. I try to leave myself a pretty good cushion on my capacity also. If I think a chunk of main trunk will go 2,000lbs, I'm wanting 3,500-4,000lbs of capacity. You have to have some wiggle room to deal with shock load from them cutting it off. I try to put just enough pressure on a limb to lift it, but not too much that it goes shooting up when they cut it, because that shock loads you too, when it springs back.
You always err on the side of cutting too small of pieces, the new tree guys always want you to take 1/2 the tree (time is $). I will make the call from the cab on how much tree to cut, the guys I work with a lot, know and understand that, its a big trust thing when they're up in the tree with a saw and buzzing through a 4' oak. They don't want it in their teeth either.