I'm not sure about the unit build weight, but I'd assume it goes off of the unit weight itself. You can usually find that informaion in the inspection window. You could either find a like unit or lay one down and then inspect it from there. You can always cancel the unit construction once you have the information. As far as the limits to construction in each region, control+click on the region's city/fort/etc. This should pop up what kind of industry you have. Some of them add naval construction points and others might add land construction points. The sum of each category is your limit. Don't forget some units like artillery or ironclads also require industry of some kind.
Rod Smart wrote:this doesn't answer your question, but its an important answer:
only build in places where you have depots! I once lost half a build in Wisconsin because I did it in a place without supplies, and had to spend replacement chits on units that weren't finished building yet
Maybe it depends on what setttings you play with? I've never really run into this issue myself. But then again, I tend to build in depots as well but for different reasons. I usually marshall my forces in a couple spots and try to keep enough of a garrison that those builds don't go up in smoke, or worse captured, to a large raiding force. Nothing sucks like losing any units, especially artillery batteries or river ironclads, you just laid down and those lessons have stuck with me.