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".)