Whether a person uses one or both eyes to align and reference a sighting system on a weapon is strictly dictated by the individual's visual ability and limitations, personal comfort, the weapon, and the shooting conditions.

Some shooters just cannot use both eyes to sight with, without seeing double pins and/or having the sight greatly blurred and off the POA. Especially, when they have but a second to aim before firing. Additionally, right-hand shooters whose dominant eye is their left eye, or left-hand shooters whose dominant eye is their right eye, generally cannot shoot with both eyes open.

I do not personally have access to factual and verifiable data, but I suspect that most shooters, which includes expert shooters, sight with one eye when using most sighting systems.