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".)
I push Rhymes like Weight
I push Rhymes like Weight"
Taken from: "Pushin Weight" by Ice Cube (again, the slang form of Pushing Weight)