Have you asked your contractor for suggestions? I'd have to see the supports and the weight to begin to guess...

can you wrap a bit of quilted fabric/insulation/ something around the support to dampen the noise? (this is just a guess as i'm not quite seeing whats going on in your under the sink photos).

Yes, that's an idea that our cabinet guy had as well. I can try that. Mostly curious if this has happened to others as well - maybe I should have purchased a different style faucet with this sink? Basically the weight rests right next to the sink support board.

Oh boy- Did you ever fix the problem?

How about taping a wrap of foam rubber around the weight?

Or you can tape a piece of bubble wrap to the back of the sink.

The weight should be sliding on the hose, not stuck in one spot. It is too tight.

The weight should be fixed on the hose at the "proper" height. If it was sliding on the hose: a) it wouldn't work properly, and b) it could cause wear on the hose.

https://www.thisoldhouse.com/how-to/how-to-install-pull-down-faucet

As far as a fix to the OP's problem, it looks like the weight catches on the sink underneath because it happens to hang too far forward. It might be possible to screw in a small piece of plywood that starts above the drain pipe and runs up behind that horizontal cabinet frame piece. That way, as the weight slides up, it runs smoothly against the plywood and doesn't bump into the sink. How thick this piece of plywood should be depends on how far back the hose and weight need to be displaced to clear the sink.

Exactly. ^

Found this while looking for a solution to a similar problem. Brand new Rohl and not enough room between sink and cabinet rear to move freely. Wondering if there’s an alternative that could use elastic instead of a weight.

I solved the same issue by placing the weight and hose line in an oven mitt then clamping the top with a binder clip. Works amazing, no sound, no wear and tear. But I am working on a more aesthetically pleasing version.