The weight of a knife is important in that it directly pertains to inertia as the the knife is put into motion, or made still.
A lighter knife will start and stop more quickly but a heavier knife might seem to, in a way, carry forward your intentions, the way a heavy object might continue to move in a line after you’ve given it a shove. A light knife requires less effort to lift and more effort to push against resistance.
A heavy knife, the opposite.
Weight distribution can be thought of as pertaining to a knife’s feeling quick like a whip, or slow, buoyant, and centered (think of the difference between two identical twins equidistant from the center on a see-saw, in one case sitting on the far ends, in the other, close to the center).
Two knives might weigh the same but have vastly different feels in the hand when cooking. Which feel is best for you is completely subjective and hugely important so make sure to try any knife you’re considering buying on food (if you can’t then at least go through the motions you normally would as if you were cooking) before you commit.
Don’t just pick it up, turn it over and shake it (we all do this and it’s stupid).
Again, trust your hands, they’ll know.
