Would we or things weigh more if the planet did not spin?

Depends. On the poles...no. At the equator, a tad less all other things equal. Why?

'cause on the poles we are not spinning around the polar axis; so there is no centrifugal force to pull us outward away from the planet.

But on the equator the spin speed is about 1000 mph, which does create a measurable centrifugal force and outward pull to partially offset the pull of gravity.