To recap -
(a) minimum V2 invariably will give a gradient less than maximum and is driven by the OEM's desire to present the aircraft in a favourable runway distance required light.
(b) if you increase V2 (a bit) above minimum V2 -
(i) the gradient will increase - initially comparatively nicely and, then, as the speed is increased further, less and, eventually, gradient will decrease. It follows that we are interested in the first section only. Looking at CliveL's graphs, we might start at a WAT limit of, say, V2min=140kt, or thereabouts, for 2.4% - increase to an overspeed V2=160kt and you improve the gradient (for the same weight) to around 3.5%.
(ii) the distance to get to the increased V2 increases - significantly - approximately (V2 overspeed/V2 min)^2.
(c) a little bit of extra speed may give you a better takeoff scenario, if the runway distance is there and the obstacles aren't too close to the runway. Clearly, though, it is a case of (rapidly) diminishing returns as the V2 is increased.
(d) end result is the usual compromise. IF you have some spare runway, AND the obstacles suit, you might be able to get a better weight off the runway using an overspeed takeoff schedule. Generally no good for close in obstacles but great for far out obstacles. This reflects the fact that the net flight path is lower until the TOD penalty catches up to the original minimum V2 gradient .. and thereafter it's plain sailing.
(e) whether you use overspeed schedules to get a higher takeoff weight or improved actual gradient is up to you (or the beancounters)