How much weight would I have to carry to equal the resistance I would face swimming in a pool of water? Let's assume I am wearing the same clothing to perform both events.
I don't see how you can get a very exact equivalence since the forces acting against you would be different, and I think that holds even if you were able to distribute the weight evenly around your body. The water resists your movement in whatever direction you move against it whereas gravity only acts downward.
Agreed. It's apples and oranges. There might be some studies done on ways of simulating swimming conditions using weights, but it won't be a direct connection, like a formula, it will be a trial and error thing. And very dependent on variables.