The verb weigh has 5 senses (first 4 from tagged texts)
1. (19) weigh -- (have a certain weight)
2. (4) consider, count, weigh -- (show consideration for; take into account; "You must consider her age"; "The judge considered the offender's youth and was lenient")
3. (2) weigh, librate -- (determine the weight of; "The butcher weighed the chicken")
4. (1) count, matter, weigh -- (have weight; have import, carry weight; "It does not matter much")
5. weigh, press -- (to be oppressive or burdensome; "weigh heavily on the mind", "Something pressed on his mind")