No it doesn’t
Go back and read the posts above, as you’re confusing the ratings.
If you’re talking about GVWR, it is only is only the weight carried by the car’s suspension. It does not include the entire weight of a towed trailer, just the tongue weight, which must be under 200 pounds for Class 1 hitch. That’s not a problem with a small trailer.
If you are talking about “rated towing capacity”, that is the weight of the trailer only, independent of the GVWR. The OP indicated that the trailer was well under than weight, so there should be no problem. I can’t imagine a trailer with a couple of kayaks on it weighing more than 500 pounds and it may be considerably less.