This is a great question. Sergeant Major Morris is not one of the main characters, but he is essential to the plot, as he is the one with the tale of the monkey's paw as well as the paw itself.
I would say that the very fact that Sergeant Major Morris had the monkey's paw and did not destroy it right away, knowing the evils it possessed, is most telling of his character. Any reader will wonder why he would even tell its tale to the the Whites if he considers them friends. To be sure Morris threw the paw into the fire at one point, but he could have done it when no one was around at home. In this way, the paw would have been completely destroyed.
The fact that Morris does not do this suggests that his character is wanting. There is something ominous about him. He might not be a good man, no matter what he says or how much he seems to care for the wellbeing of others.