That helmet is called a helmet-mounted display, or just HMD.
It offers a display much like the HUD in front of the pilot.
So when they look away from the HUD, vital information moves with them. Including targeting information. And even FLIR overlays.
Some models even allow the pilot to select a target by just looking at it. Like the Eurofighter.
As for the weight, those helmets are primarily made of carbon fiber, very light weight, strong, and expensive.
Any CG offset can be balanced by adding a counter weight in the back of the helmet.
In more modern planes, like the F-35, the HMD can also overlay camera displays, so when the pilot looks down at their legs, they can actually see what's under the plane. To achieve this the camera feed is only shown to one of the eyes.
That's the F-35 helmet. $600,000. A VR headset on steroids.
Here's a video explaining it.