You can get a "binding" estimate. That way they cannot charge you more than what they guess your stuff will weigh. Of couse this esimate will be a bit higher than if you had requested a non-binding esimate, but worth it in my opinion. When they do the estimate follow them through your house to make sure the "tag" every thing you are brining with you, and nothing you are not. For moves across state lines there are a bunch of federal rules they must follow, so in theory your chances of getting ripped off are less than that of a "cross-town" move. Ask about boxes, some will bring you boxes to pack your stuff free of any extra charges, some will direct you to the back of a local store to grab some used ones...

EDIT: here is a guide

Monstermoving Mover Rights Guide (PDF)