Stabilizer

In archery, a Stabilizer is a counter-balance weight intended to help shooters keep a bow steady when shooting, as well as reducing hand shock, bow noise, and bow vibration. Stabilizers are made out of various materials, the most common found in modern bows being carbon and ABS plastic, and can be specially designed for either hunting or target shooting.

A medium length hunting-bow Stabilizer appears in Battlefield 4 as a permanent attachment for the Phantom compound bow.

Battlefield 4
"Improves accuracy by providing additional balance and stability while reducing hand shock, noise and vibration."

- In-game description

The Stabilizer is a weapon accessory exclusive to the Phantom in Battlefield 4. The attachment acts as counter balance for bow, and allows it to be incredibly accurate when shot while aiming down sight. Similar to integrally suppressed weapons like the AS Val with its Suppressor, the Stabilizer is permanently attached to the Phantom and is the only attachment available in the accessory slot.

The Stabilizer in fact has no attachment entry in the game files and is actually modeled onto the Phantom, so it's existence is primarily to justify the bow's high accuracy in-game.