The phrase "weighs heavily on your conscience" might have more truth to it than you think. Latest research reveals that people who think about horrible things they might have done in the past felt like they weighed more than they actually did:
In the study, two researchers, Martin V. Day of Princeton and D. Ramona Bobocel of the University of Waterloo, asked subjects to remember unethical and ethical things they had done. Then they had the subjects say how heavy or light they felt. Specifically they asked them “Compared to your average weight, how much do you feel you weigh right now?” on a scale of 1 to 11. People who were asked to recall past transgressions actually felt heavier than those who recalled an ethical act—or the control group of those who weren’t asked to recall anything at all. The authors argue that the extra perceived weight is the weight of guilt.
So there you have it, scientific proof that carrying all that emotional baggage really does weigh you down. Maybe you'd be better off just coming clean and getting that guilt off of your chest.

[Bloomberg Businessweek]