Do heavier subs generate more wake, design & velocity constant?
No, or not exactly. Mainly because there is no such thing as a heaver sub for a given displacement, at least while submerged. Subs pump out or take in water so as to remain the same weight as the water they displace. A submarine does not fly through the water, it floats like a blimp. A blimp though can use some aerodynamic lift to change altitude. A submarine can too for that matter, that's what they do when they swim down or up, using the diving planes (and the hull) to generate hydrodynamic forces to aid the boyancy force to change depth more rapidly. A physically larger sub will generate more wake than a smaller one, but a weight difference between two subs of the same design just won't exist under normal, submerged condition.