Your deportable under 237 for that possession of marijuana charge, since it was over 1oz. Doesn't matter that it wasn't a felony, it is a conviction.
On the brightside, it sounds like you were under 18 years old when the crime happened. I'm pretty sure that you would have to have been convicted in a adult court, and that it would have needed to involve some violence.
You might try looking online for the "Federal Juvenile Delinquency Act" but I'm not sure that applies to drug crimes. The problem is most of my information deals with inadmissibily. You might also look up INA 237(a)(2)(A)(iv)
I did find this is some old notes...
1. Youthful Offenders
There is an exception to INA § 212(a)(2)(A)(i)(I) for an alien who committed only one crime if the crime was committed before that alien was 18 years old, and the crime was committed more than five years before the date of the application for a visa or other document and the date of application for admission to the United States. INA § 212(a)(2)(A)(ii)(I). This exception concerns the "committed" date not the "conviction" date.
Juvenile court adjudications of guilty are not convictions. Matter of Devison, 22 I. & N. Dec. 3435 (BIA 2001). To determine whether a juvenile proceedings results in a criminal conviction or civil delinquency adjudication, the BIA compares the judgment in question with adjudications under the FJDA (Federal Juvenile Delinquency Act). In Devison, the BIA concluded that the new York youthful offender statute was similar in nature and purpose to the juvenile delinquency provisions contained in the FJDA. In contrast, in Uritsky v. Gonzales, 399 F.3d 728 (6th Cir. 2005), the Sixth Circuit held that the grant of youthful trainee status under Michigan’s Youthful Trainee Act qualified as a conviction for immigration purposes since it was more analogous to a rehabilitative expungement. In Badewa v. Attorney General, 252 Fed. Appx. 473 (3rd Cir. 2007), the court concluded that a conviction for assault with a dangerous weapon and carrying a pistol without a license under the District of Columbia Code’s Youth Rehabilitation Act (DCYRA) was a criminal conviction under the INA.
While a juvenile delinquency is not a criminal conviction on which to base removal or bar relief from removal, an IJ reviewing an application for a discretionary benefit, such as adjustment of status, may consider the juvenile offense as a factor in evaluating whether to grant the immigration benefit as a matter of discretion. Wallace v. Gonzales, 463 F.3d 135 (2nd Cir. 2006).
I think you are going to have to man up and spend a few bucks talking to a good immigration lawyer...