Sure I'm not a pilot, but we were advised in good ol' ATC school - (I did the course at the now defunct Henty House, Melbourne) that weight of the vehicle had no bearing on aquaplane speed.
Aquaplane speed was a function of tyre pressure and speed, and that weight (or mass) of the vehicle had no effect. Hence, the advice to thump it down, because there was therefore more mass exerting force on the tyres would be incorrect.
We were also advised that to determine your aquaplane speed roughly (in mph), you take the square of your tyre pressure (in psi) and multply by 9. Hence if your tyre pressure is 25psi, your rough aquaplane speed is 45mph. Hence most cars will aquaplane at 80kph. I've managed to have it occur to me while driving through a large puddle at 90kph.
The reason we were advised about this using the old imperial measurements was because the film depicting the experimentation on aquaplaning was done by NASA. It showed a B1 thumping it down, then slowly drifting off the runway.
Tread pattern will make little difference, but grooves in the runway allow the surface water on the runway to drain quickly and help reduce the incidence of aquaplaning.
Correct me if I'm wrong, but I'm sure the info I received way back then is still correct.