Are golf balls different weights?

Only by tiny amounts.

The R&A and USGA equipment rules say a ball must not weigh more than 1.620 ounces, which is 45.93 grams. There is no minimum weight, so a maker could sell a lighter ball if it wanted to. In practice the big brands build close to the limit, because a heavier ball holds its speed better through the air, so the balls on the shelf differ by fractions of a gram rather than anything you could feel.

Size works the other way. A ball must be at least 1.680 inches across (42.67 mm), with no maximum. Makers stay close to the minimum here too, because a smaller ball cuts through the air better.

The rules also require the ball to be spherically symmetrical and to pass an initial-velocity test and an overall-distance test on the governing bodies’ equipment.

What does vary between balls is what is inside: core firmness, layer count, and cover material. Those change feel, spin, and launch far more than any weight difference you could measure at home.