Collocations for weigh - verb

carefully
up
The jury weighed up the evidence carefully.

against
We weighed the cost of advertising against the likely gains from increased business.

heavily, strongly

against
His untidy appearance weighed against him.

in favour/favor of
This fact weighed heavily in her favour/favor.

with
His evidence weighed strongly with the judge.

Weigh is used with these nouns as the object:
anchor, benefit, evidence, merit, option, risk, situation