There is a Supreme Court case called Padilla v. Kentucky that says that if your attorney on the drug case failed to inform you of the immigration consequences of pleading no contest to marijuana possession, you can request that the court reopen your criminal case on a basis of ineffective assistance of counsel. I highly recommend consulting criminal defense attorney familiar with Padilla and its possible impact on remedying the immigration consequences of your plea. Otherwise, with that plea of no contest to misdemeanor possession, and the amount of marijuana involved was more than 30 grams, you are inadmissible to the United States. The only waiver available is as a nonimmigrant. Marriage will not cure the conviction or make you eligible for a waiver.

If, however, the plea stays (i.e. you cannot get it reopened and dismissed), and the amount involved was less than 30 grams, you could apply for a waiver, either as a nonimmigrant or an immigrant. I highly recommend consulting, first a criminal defense attorney regarding your no contest plea, and an experiences immigration attorney regarding how to apply for the necessary waivers, should that become necessary.