It is aeronautics that gives us the capital G for the multiples of the 9.81 m/ss acceleration or its associated force, regardless of the writing conventions of national or international systems of units. That is, a jet fighter's turning ability is more often described as +7G than as +7g.
But conventions vary. The "gold standard" Aviation Week & Space Technology
is consistent in its use of lowercase in expressions such as "g-forces" or "+2.2g", while otherwise observing the Imperial system of units and its writing practices (no fear of confusing it with "gram", then!). But even AW&ST
speaks of G-LOC (acceleration-induced loss of consciousness), which certain medical magazines in turn call g-LOC. Basically any "popular" publication on aeronautics is going to go with the uppercase G for describing accelerations...
I honestly can't remember - has Star Trek ever used "gee" for acceleration in any context?