A conviction for possession of marijuana (not sale) less than 30 grams of less will, generally not bar your application for green card, especially as the spouse of a US citizen. The other issue regarding your lack of income can be resolved if you have a friend, co worker or relative to act as a co-sponsor for your I-864 Affidavit of support.
Answered on Dec 23rd, 2013 at 4:53 AM