I think they all have huge burdens, but I think maybe Edward and Alice have the biggest burden. Both of them are given information that isn't available to others, and they can't always know what to do with it or how to use that information morally. Edward is privvy to everyone's thoughts, so it has to get difficult to remember who said what and who thought what.
But I think Alice might have it just a little bit harder, because she might know what's going to happen and feel the need to change it, but A.) how can she know what exactly she would need to change and B.) how can she know that the change is for the better?
While I agree that feeling other people's emotions is probably a huge burden for Jasper (don't you just want to cuddle him to make him feel better?) at least he has the ability to make them feel differently and improve the situation.