Guys,
All of you who claim the OP will be able to sail through the N400 process, maybe you will think again after coming across this posting this morning. See the link and read what the wife said about her husband with a drug possession of 3/4 of weed from 1987 or so. (I might be incorrect about the time frame).
http://forums.immigration.com/showthread.php?t=303151
Actually, I think it was 1 and 3/4 oz (that is 7/4 oz), or about 49 grams of marijuana in the post you cite. As I remember, a single conviction for marjuana possession below 30gm is not considered deportable, but anything above 30gm or a conviction on any other drug charge (e.g. intent to distribute) does make one deportable:
"(B) Controlled substances
(i) Conviction Any alien who at any time after admission has been convicted of a violation of (or a conspiracy or attempt to violate) any law or regulation of a State, the United States, or a foreign country relating to a controlled substance (as defined in section 802 of title 21), other than a single offense involving possession for one’s own use of 30 grams or less of marijuana, is deportable.",
http://www.law.cornell.edu/uscode/8/usc_sec_08_00001227----000-.html
So perhaps the amount made a difference here. Still, it is rather surprising that they decided to initiate deportation proceedings for such an old and fairly minor drug conviction...