If you know the thickness and weave count it might be easier to find. An 8x8 weave per square inch with an 8 mil. thickness would be light in my book, but that's usually billed as a middle weight. You can get 8x8 with 5 mil. thickness in the blue tarp range.

Anyway, search by weave and thickness if you know the stats on what you have now and you should be able to find what you're looking for.