What is Vg in this VG diagram?
It is the maximum speed in gusty weather. Aircraft designers and certification authorities make assumptions about the maximum vertical gust an aircraft will encounter and design the strength of the wing spar for it. Here 24 feet per second are assumed.

Depending on the mass of all parts not creating lift (fuselage, vertical tail, pilots, equipment ...) the load on the wing spar varies with the aircraft mass. For that reason, lighter aircraft can afford to enter a gust at a slightly higher speed. Here, the 800 lbs glider may fly up to 150 MPH, while the 40 lbs heavier glider should stay below 147 MPH to suffer the same wing spar bending loads when flying into this 24 fps gust.

Flying faster means flying at a higher dynamic pressure and at a lower angle of attack. Entering a gust will increase the angle of attack by the ratio between gust speed and flight speed. Since dynamic pressure is proportional to the square of flight speed, a linear wing lift increase due to higher flight speed will remain when entering a vertical gust. Also, at lower speed the angle of attack might be high enough that the angle of attack increase due to the gust will stall the wing, putting a natural limit on the load increase. Flying faster will remove this load limitation.

The maximum flight speed in gusty weather v$_g$ is a limit speed just like v$_{NE}$, but applies only in specific weather conditions (admittedly those which are most suitable for glider flying). While v$_{NE}$ might be determined by a minimum flutter margin, a formula in the certification requirements or structural loads in maneuvers, v$_g$ is determined by the maximum load factor the aircraft can tolerate.