Other than being controlled by field length, maximum $V_1$ is also controlled by $V_R$ (Speed for rotation) and $V_{MBE}$ (Maximum brake energy speed). $V_1$ must not exceed either.

This means that at low gross weight, _theoretically_, if the aircraft had not yet been rotated past a $V_1$ limited by $V_R$, sufficient distance _may_ still exist to stop the aircraft on the remaining Accelerate-Stop Distance Available (ASDA).

At higher gross weights, $V_R$ will increase, also allowing for a higher $V_1$. Therefore, in response to: "So why isn't V1 reduced to allow for better stopping?": The higher $V_1$ still provides adequate margin for stopping on the ASDA, but gives you the _option_ to abort the take-off at a higher speed.