Superman and kryptonite

If Superman can barely lift the kryptonite out of the water, how can he fly with it and stab Doomsday? The whole heroic and selfless act is undermined by this inconsistency – especially since these scenes happen one after the other.

It can be argued that it was sheer will, or that it was the momentum, or some other thing. But Zack Snyder further emphasized a point when Lois dragged Superman out of the water – kryptonite is his biggest weakness. To have him immediately pick up the spear and impale Doomsday seems baffling – how much strength was needed to penetrate his skin?