From statement 1, we get: $A \& D > B, E \& F$

As none of them is the heaviest, we can conclude that C must be the heaviest. So, statement 1 alone is sufficient.

From Statement 2, we get: $C>A>D$

Using statement 2 alone we cannot determine the heaviest item.

NOTE: Official answer is "C or D", but logically A should be the correct answer.