The 'g' limit is another way of specifying a limiting acceleration. Accelerating the airframe applies loads to it. One 'g' is an acceleration of 9.8 m/s/s. If the limit is 3 'g the the aircraft mustn't exceed 3 x 9.8 m/s^2.
At a given weight & speed elevators can apply a certain maximum force to pitch the a/c. This, in turn, causes an increased AoA leading to increased L (ie a force) and a resulting acceleration to the airframe. If speed is increased then the sequence will result in an increased acceleration ie a greater load. If speed is reduced then the sequence leads to a lower load. Starting at low speed - ie below Va -the wing will reach its critical AoA before the limiting acceleration is reached. As speed increases then the airframe experiences more & more load prior to the wing stalling. Increase speed enough & the airframe eventually reaches its limiting load just as the wing stalls. Any faster & the limit will be exceeded prior to the wing stalling.
Since this is all about accelerations & the forces that cause the acceleration then mass also is a factor. A given force will cause a greater acceleration the lower the mass. The L force goes up by 'X', accelerating the mass of the whole aircraft. The lighter the aircraft then the more it will be accelerated for the same increase in L. Max Va is at max weight because the heavier aircraft can't be accelerated as much by the increased Lift as when it is lighter.