I own a Fujifilm GF670 (non-W). Frankly, I believe that part of the "flimsy feeling" perception is due to the very nature of the camera's design. After all, when opened it's simply a bellowed container of...air. Personally, I've found it to be a finely engineered camera, not flimsy at all. But compared to the more massive slr-style body of a Mamiya 7 the GF670 will feel like air, containing only the most fundamental elements of picture-takin'.
Fun anecdote: I was recently walking through a department store when I spotted what looked like an older model of the Fuji folder on a counter some distance from me. As I approached I noticed that there looked to be not one, but TWO, of these cameras on the counter. This store had nothing to do with photography but, damn, those cameras looked to be in pristine condition! Erp!...They were bookends molded to look like "antique" cameras.