Oxford American Dictionary:
heavy hitter noun informal
1 an important or powerful person : a high-profile national issue pitting heavy hitters in the Senate against the Department of Agriculture.
[color=blue]2 a high-scoring athlete.
The only sports I know of where you hit are boxing, baseball and cricket. You don’t hit people or things in soccer, track, basketball or swimming.
The PR firm referred to in the quotation was not hired merely because they punch a lot, but because they hit hard and are successful. You could conceivably imagine a boxer, but when it comes to corporations and PR firms, I assume they are hired not only for their aggressiveness, but also for their quick thinking, their ability to read the psychology of the opponent, and to deal with unexpected situations (which we would call “curve balls”), and to get spectacular results with great efficiency. This fits the profile of what we call heavy-hitting baseball player.