The amount of weight carried by that tire will dictate to a large degree, how much water will be moved.
I disagree sir! If you want to be pedantic then .........maybe as the tyre footprint is larger with increased weight but everything else I agree with.
When I went to pilot school (1963) the formula was aqua/hydro plane speed equals nine times the square root of the tyre (tire) pressure. in knots
I remember watching a movie (B4 video) of hydro/aqua planing being demonstrated in a test facility through a glass plate underneath the tyre (Tire) footprint. Very interesting.
Thus for example while racing my old classic
www.targaflorioteam.org in the wet I put as much pressure in the tyre as it would safely hold (Trade secret).
If you take a normal road car tyre, regardless of tread and put say 36 psi of tyre (Tire) pressure in it will give you a hydro/aqua plane speed of 54 Kts or 62 mph or 100 kph.
Believe me it works in torrential rain.
Chok Dee