If the marijuana case was dropped or dismissed it will not cause a problem with your reentry into the U.S.
Beware. Possession of marijuana even without a conviction may render you in admissible to the U.S.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
It should not cause any problems, as it is a misdemeanor, with a dismissal. I would try to get it Expunged, however, it would not be completed by March, but would be for the future. I would seek the advise of an immigration attorney to be more confident.
Every request for admission to the US by a non-citizen (and that includes Lawful Permanent Residents) is at the discretion of the immigration officer interviewing you. Although your possession of cannabis charge was dismissed, there is a provision in the Immigration and Nationality Act that says that where an appropriate immigration official knows or has reason to believe that the alien is a trafficker in controlled substances at the time of admission to the United States, admission can be denied. There are other concerns as well so I would be very careful. Consult a local immigration attorney.