Can you post a pic? Agree, it sounds like Caulerpa (there are quite a few types). If you're seeing a long horizontal piece with root-like attachment and 'leaves' (bubble, cup, feather, blade or another shape) growing vertically, I'd say you're looking at a Caulerpa species. Chaeto looks like steel wool, or spaghetti in a ball -- no stems, no leaves, just one looooooong thread-like piece.