According to ASME Y14.5, a general tolerance block covers "all dimensions on a drawing for which tolerances are not otherwise specified" (paragraph 2.1.1(e)).
And paragraph 1.3.22 defines a dimension as a number "used to define the form, size, orientation or location, of a part or feature."
So putting those two ideas together, weight doesn't fall under the definition of a dimension, and thus the general tolerances wouldn't apply to the weight.
John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems