"gives weight" is correct and usable in written English.
You can use it whenever you want to express that something is important or influential. For example: "His credentials give weight to his opinion."
Comedy humanises: the light touch gives weight.
That gives weight to allegations of selective justice.
He's capable of suffering, a quality that gives weight to the bounce in his stride.
But suppose I were to ask what gives weight to that material.
Mr. Nouvel's creation gives weight to an underappreciated history while remaining firmly pointed toward the future.
Their version gives weight to the aspirant mogul's "dreams of grandeur" and "megalomania".
(Game score gives weight to complete games, which have become increasingly uncommon since 1980).
Having a background in law and social work gives weight behind the help that I give them.
That Ertekin served only a few weeks of a four-year sentence gives weight to this theory.
Connecting with an inmate gives artists a face and a storyline that gives weight to the issues involved.
An unworldly Zen teacher with a touch of very earthly cruelty, there's authority to her screen presence that gives weight to Strange's spiritual journey.
