Could I develop asthma from smoking weed also?

Possibly. Technically speaking, asthma is usually an allergic condition. That is, the symptoms develop due to allergies to pollens, mold, etc. However, about 10-15% of asthmatics are non-allergic, and tobacco or marijuana smoke can both make such symptoms worse. The smoke from marijuana is typically non-filtered as well, making it particularly dangerous to the lungs.
Yes. Smoking anything can give you asthma, or more commonly exacerbate an underlying asthma that may have been ok before. Think about it - whatever you inhale, goes right to your airways and irritates them!