Although both Utterson and Enfield protest that they prefer to mind their own business, why do you think that both men are so interested in finding out more about Mr. Hyde?

Enfield has a natural curiosity about him. When he sees Hyde after he's trampled over the young girl, he's both repelled and fascinated by him in equal measure. There's an air of mystery about this strange, repulsive character, and it's only natural that he should want to find out more about him. In particular, Enfield wants to know why Hyde was able to open a strange door with a key and then suddenly emerge with another man's check as compensation for the child's injuries. There's clearly more to this case than meets the eye.
Utterson, though considerably more logical and rational than his friend, is equally fascinated by the case. As a lawyer, he's particularly drawn to the potential element of blackmail involved. If this is indeed a case of blackmail, as he suspects, then it's a very serious legal matter, one with which Utterson might want to deal. Though neither man has the faintest inkling of just how strange, and utterly terrifying this case really is, there's more than enough mystery to keep them intrigued. And though they agree not to discuss the matter further—and shake on it—we know that their fascination with what they have seen will endure.