Most of the time difference in weight paint behavior between Blender and Unreal comes down to accidently adding weight to non-relevant bones like control or mechanism bones etc. You want to click on the individual vertices that are misbehaving and make sure only intended deform bones have influence on them. This is almost ways the cause.
Other things you’d look at is to make sure verts are not influenced by too many bones. Up to 4 bones to be efficient or max 8 bones per vertex. Also check you are not using Blender specific features like bendy bones or possibly some kind of deform modifiers etc.