Science doesn't deal in truth -- it deals mainly in (empirical) evidence. Nor does science prove theories -- it decides between alternatives.
Newton gathered enough evidence to infer his theory of gravitation was much, much better than any of the alternatives.
P.S. IIRC Newton's evidence involved celestial bodies, not weights in a laboratory. (although I imagine some data was gathered by the attraction of masses to the Earth) I don't believe they didn't have tools sensitive enough back then to measure the gravitational attraction between laboratory masses.