If you were to take 9- 10 yards of a 5.5 to 7.0 oz linen, (Around $5-6 a yard at Sew Fisticated in Sommerville, or slightly more on line.) wash and dry it several times and then sew it into a baffled quilt with poly pellets as the filling, it should be heavy enough for your purposes and still breath well. It will be machine washable and will get softer with each wash and dry cycle.

Cotton would work, but it will not breathe as well as linen does on the muggy nights and it does not dry out as quickly during the day.