1
general::
Act the part of a villain; take the blame for unkind behavior. For example, She can't bear firing an employee, so she relies on Jim to play the heavy. This colloquial term comes from the theater, where heavy has been used for a stern, serious role or that of a villain since the early 1800s.
American Heritage Idioms
2
general::
Phrase(s): play the heavy
Fig. to act the part of a mean person; to do the unpleasant tasks that no one else wants to do. (Refers originally to playing the role of someone evil in a movie, etc.) • I’m a nice guy, but at work, I am required to play the heavy. The boss makes me do all the cruel things.
McGrawhill's American Idioms And Phrasal Verbs