Which is why you should run your front tyre inflated to whatever pressure lets it deflect the same as the rear, which is generally about 1.5bar less on a roadbike, 1bar less on a mtb.
The difference in air pressure you would normally use is only enough to equalise the deflection when your weight is distributed normally. Shift your weight back further than normal and the front tyre will be over-inflated then.
If you have the front tyre soft enough to be properly inflated when your weight is well back (further than normal), it will be chronically under-inflated for normal riding.
Some weight is transmitted by the frame to the front wheel when you put it on the pedals, but more weight goes to the the front wheel when you put it on the bars.
In some situations, it is dangerous to reduce the weight that goes on the front.
Yebbut how much can you change your centre of mass by hoiking back in the saddle (unless practicing mtb/dh stylee bum over the rear wheel - which isn't easy with a saddle at the correct height).
Couple of inches back?
Putting your weight through the bars or though the pedals cannot change how much you weigh, or where it affects the bike - the front wheel.
It can
feel as if more weight goes onto the front wheel, because you are using your relatively weak arms to support your body, not your incredibly strong cyclists legs. The adverse effect on how the front wheel tracks also seems to support this idea, though that is a misinterpretation of causality - the steering goes heavy and hard to move because you are keeping yourself on the bike with the same muscles as you are trying to steer with, not because all your weight is going through the front wheel.
Just to make sure we haven't crossed wires, when I said taking your weight through the pedals, I didn't mean get back in the saddle, I mean cocking the pedals to horizontal and supporting your weight through your legs, without really changing your body position backwards.
Weighting the bars as you brake is more dangerous than weighting the pedals - because if you lock the front wheel, with your weight on the bars, the front will disappear from underneath you, pushed away by your own weight. With weight on the pedals, you have a *small* chance of catching the bike, as your weight isn't being borne by the steering.
BTW, I am fully prepared to accept I'm wrong if someone can wade in with some facts n figures to disprove me.