Our son was always weighed with diaper on. His weight was never an issue, so that might be why. Also, he was miserable in a wet diaper until recently, so we couldn't have weighted him wet. I'm also thinking that until he was around 2, he never really did so much in a diaper that I would think it would have affected his weight. Now he really fills a diaper, but mostly at night.
Next time, if you think the diaper is too saturated, can you ask to change your little one first?
Happy Healthy and Handsome DS 8/13