Explanation:

- We have five objects: A, B, C, D, and E, all with different weights.

- Statement 1: The weight of B is double the weight of E.

- Statement 2: The weight of C is three times the weight of A.

- Statement 3: The weight of D is four times the weight of C.

- Statement 4: The weight of B is half the weight of D.

Let's analyze:

- From Statement 1: $B=2E$

- From Statement 4: Since $B$ is half of $D$, it implies $D=2B$

- From Statement 3: Since $D=4C$ and with $D=2B$, it aligns perfectly in this way: $B=2E,D=4C,2B=4C$

- This all simplifies to: $D$ being heaviest since it doubles $B$, which is already a multiple of other weights.

Thus, looking at all given statements, D is indeed the heaviest.