Why base current changes with collector emitter voltage?
When you saturate Vce (down near zero), the transistor's current gain drops greatly. So the base-emitter junction becomes "just a diode". Green curve hasn't quite reached Vce saturation. Blue curve ventures into saturation.
Perhaps you are trying to investigate the "early effect" as G36 has suggested. This effect addresses a linearly-operating transistor. While your circuit is driving this transistor hard, the green-curve drive is at the very upper edge of linearity. The blue-curve drive is over the edge of linearity.