It has been unclear to me why Lord Barkis kills Emily in Tim Burton's Corpse Bride. We only know that it happens.
I think this was very well explained in the movie. His whole m.o. is to find a rich woman and either marry her or convince her to run away with him and her dowry. He then kills her, inherits/steals her wealth, lives comfortably as a rich widower/bachelor until the money runs out and then repeats the whole process. It's shown that this happened with Emily and now he plans to do the same with Victoria.
In the case of Emily, this is basically spelled out in the song Remains of the Day, with Barkin being the "mysterious stranger" who convinced her to elope with the family jewels.