It depends on how much you weigh. Yes, it is supposed to tighten when you sit on it, but im not sure that it should be getting loose when your riding.
Try to Tighten your chain, get to top speed on about 3rd or 4th gear and check out your chain to see how its doing. then when you stop, notice if there is any change in the chain. beacuse when your going slow on your bike, you chain is not getting pulled as hard. when you get to higher speed it usually get pulled tighter.
Hope it helps
DBM
