These two adjectives are not related except for the shared prefix -over, which means “too much.”
Overweening means “overly arrogant, ambitious, or proud.”:
Donald’s overweening desire to own the world will be his downfall.
Overwhelming means “too much to handle, process, or deal with”:
Working and attending college while being a parent must be overwhelming.
Patricia felt an overwhelming concern for the well-being of her baby.
Overwhelming is not necessarily bad; people can feel overwhelmed by kindness, love, generosity, or blessings. Overwhelmed merely implies a temporary loss of control over one’s feelings, because of too much stimulation.