The input-output weight enumerator of a convolutional code characterizes the distance spectrum and allows error probability bounds to be conveniently evaluated. To efficiently compute the weight enumerator, Pimentel recently introduced the so-called state reduction algorithm which has a convenient implementation using existing symbolic mathematical software. In this paper, we propose a dynamic state elimination ordering heuristic to further accelerate the algorithm. As demonstrated by our empirical results, the accelerated state reduction algorithm can achieve impressive complexity savings relative to the original algorithm when applied to compute the weight enumerators and its various truncated versions of convolutional codes with moderate-to-large constraint lengths.