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2.
Usually written in standard English as "Pushin' Weight," this phrase was popularised by Ice Cube (the great) who proclaimed that "Yeah Yeaaaaah-" he in fact "pushed rhymes like weight."

The phrase, a combination of the two root words, "Push" and, well..."weight," is a milestone in urban language. The former is an American slang term most commonly used to refer to the action of dealing (e.g. drugs) in a semi-forceful way. The latter word of the phrase is defined throughout this glorious site as cocaine, which as Rick James informed us, is "a hell of a drug" (see also "blow", "yaio".)
"Yeah Yeah

I push Rhymes like Weight
I push Rhymes like Weight"
(4X)

Taken from: "Pushin Weight" by Ice Cube (again, the slang form of Pushing Weight)
by D.A.D. September 12, 2006
 
1.
to distribute large amounts of narcotics.
nigga got a S500, he must be pushing weight.
by ep June 12, 2003