How much weight can a 1x2 hold?

Answer 1

Someone said "not much" and went on to break the stick - on the thin edge, the 3/4" part. (A 1x2 is actually 3/4" x 1 /12")

Yep, breaking on the thin edge is twice as easy as on the thick (1 1/2") edge. If your question is really how to make your project strong enough, consider how to keep the weight or pressure on the thick edge, not the thin edge. Also, you can have more than one pieces of 1x2!

Suppose you are making a ramp and reinforcing the plywood with 1x2 on each underside edge. Screwing the plywood to the 1x2 will hold it such that the 1 1/2 part is being used, and having two pieces might give you the strength you need. Or try three pieces.