Why would a reduced front ride height put more 'weight' over the front axle?
At static, it won't. Adjusting ride height will only affect crossweights when measured on the scales by jacking one corner or the other. In fact, raising the ride height increases the pressure on a given wheel at static. Very rarely are cars static on the track, unless you stopped, of course. Think of a table where you want all of the legs an equal length. If one leg is shorter than the others the table will have less weight carried on that one leg compared to the others. Now, when you tip that table(like a car does in a turn) so the short leg is on the ground the table now leans toward that side. No, the total weight of the table hasn't changed, but the load or weight on each individual leg has and now the short leg has more weight on it and the leg opposite it now has less weight.
'weight' = M*g = M*9.81, unless you are counting the lower front end to be closer to the earths core and therefore more under the influence of the earths gravitational pull then a lower front will not encounter any more 'weight'.
An entertaining thought, but no the proximity to the core isn't in play here.
Similarly, 'peak grip' (at least in one degree of freedom) can be calculated by friction coefficients of two bodies multiplied by a force (mass in this case) in the axis we are measuring;
Fmax = Mu (COF) * Fnominal
So weight over the axle of the wheels is beneficial in terms of overall traction.
That assumes the level of traction increases linearly with loading. It doesn't. If that were true a 2000kg car would have higher peak grip(assuming the same tyre size, spring rates, etc) than a 1000kg car. That isn't true either. Yes, a tyre does gain grip with increased load, up to a point. This point is different for every tyre and the point where traction falls off is dependant upon many factors. As the load increases at some point the sidewall will begin to distort and lose traction. Increased load also produces increased temperatures. Every tyre has an ideal temperature range, and as the temperatures increase beyond this range the compound gets greasy and loses grip. The more loading on the tyre the sooner this happens in a turn. There is a lot going on and I could type up a book on it, but those are a few factors.
If you want another good one, all ride heights equal, crossweights equal, and f/r disribution equal; putting a stiffer spring rate on one corner(of the same height as the other 3) will result in a proportionately increased load at the surface on that one tyre during a turn.
Again, think of the feeling as you pick up the throttle for corner exit and the front begins to develop more grip. This is occuring because the acceleration of the car is transferring weight off of the front axle(reducing the weight/load on that axle) and onto the rear axle. There is only so much traction available(think friction circle) and as you pick up the throttle for corner exit you are taking load off of the front axle, thus freeing up more available grip. This only applies if you are driving near the limit. If you aren't getting anywhere near the limits of adhesion in cornering, then this transferring of weight around isn't going to have a great effect. Much as adjusting the brake bias isn't going to change much if you aren't nearing the traction limit under braking.