give weight to something
add weight to something

But first, they must add weight to whatever it is.

It's small enough not to add much size or weight.

Only a few got through to add their weight to that of the attack on the ground.

In changing themselves they added their own weight to the effort by which the world itself might be changed.

He leaned forward as if to add weight to his words.

I didn't think it was a good idea to add my weight to hers.

Perhaps he would be an ally, someone to add weight to her own words.

These add weight, but also a good bit of protection against the elements.

The boy was too heavy to add his weight to theirs.

She leaned forward slightly as though to add weight to her words.