Water Heaters - water heater leak something new

I have read the posts about water heater leaks and have not found exactly what I'm looking for. The water heater in our new house leaked. Then it didn't. It also didn't make hot water. I replaced the top and bottom heaters and thermostats in the 50 gallon short tank. It made hot water and still does. Then it started leaking. I noticed that the TPR valve was leaking, through the valve, so I replaced it. That still leaks. The pressure in the rest of the house is not that great. I haven't tested it, but it is not really very high. The temperature on the two thermostats is set at 125 degrees. We put a bucket under the valve outlet. The bottom of the tank leaks. The problem is that it leaks only when hot water is running. It doesn't leak a lot, but the spread of the water on the concrete clearly expands when the water is running and contracts when the water isn't running. It seems like it should be the other way around. There is no leak around the top fittings or around the TPR valve. What is going on?

Get a bright flashlight, a small inspection mirror and a screwdriver to probe around. Double and triple check all fittings and connections including where the elements screw into the tank. Be sure to look at inlet, outlet, anode, t&p, and drain valve. Also check where the flanges are welded to the tank (not usually easy to see). Have someone open and close faucets if it only appears while usage occurs. I have seen fittings leak momentarily after a faucet was closed.

Like I say, keep looking, it has to be leaking from somewhere. While it is unusual for a new(er) water heater tank to leak, they sometimes do.

I should have pointed that while the house is new to us, the water heater is old/er.