When two things pull you different ways, the one that outweighs the other is the one that matters more — more important, more serious, more valuable. The benefits outweigh the risks. The cost outweighed the fun. This is the sense you will meet in essays and advice. Underneath it is a pair of scales: one side goes down because it weighs more. Though actually the older, physical sense is still alive — if this box outweighs that one, it is heavier — but students meet “matters more” far more often. It is formal enough for school writing and still fine in ordinary talk. It does not mean “weigh something outside.”