Consider a simple regression (normality not assumed): $$Y_i = a + b X_i + e_i,$$ where $e_i$ is with mean $0$ and standard deviation $\sigma$. Are the Least Square Estimates of $a$ and $b$ uncorrelated? 


Question: What role is a "Heavy" supposed to fill?
Answer: Think of them as a heavy weapons team in certain games or in real-life combat:  Relatively low mobility, but high damage output, specialized/explosive/armor-piercing weaponry, and suppressive fire.

As you said, Assaults fill a "tankish" role as well as a scouting role.  Heavies are the only class other than snipers that can shoot their primary weapon twice in a turn (with associated skill), which should indicate they can be more useful when used in a defensive capacity.