What size of skateboard should I use for my weight?

It doesn't matter what your weight or height is, unless you're a child. Your height and weight tell me you're teenage, so any board will do. It's more about what you want to use it for. Smaller boards with smaller wheels and slower bearings are good for street skating and street tricks. It's easier to maneuver the board with your feet, and lighter so you can get more air and get it up easier. If you're into vert skating, quicker bearings are better as vert is really about speed resulting in bigger air and longer and more elaborate tricks. If you're using as transportation or just to ride, without tricks or anything fancy, then a wider board with big wheels and quick bearings is your best bet. The bigger wheels will handle cracks better and the wider board is easier to stand/balance on. But in the end, it really comes down to what you're comfortable on. If there's a skate shop near you, ask them to grab you a couple and stand on them to see what you like the best. If a wide board is too big, go narrow. If you think the narrow is hard to balance on, go wide. There are guys who skate street with wide boards too. I ride street, and I go with a standard Element board, Ricta or Autobahn 52mm wheels, Venture superlight low trucks, and lucky ABEC3 bearings. Oh, a note about trucks. Lower trucks make it easier to balance, because you're not wobbling so much because you're lower to the ground. But keep in mind, if you get big wheels (think 60mm), then you'll need either high trucks, or low trucks and extra risers, so when you turn your wheels don't rub against the board.