I have observed in the Shuls I Daven in that the one who does Gelila often puts the belt (gartel) on the top third of the Sefer Torah. Is there a reason or source for this? Why not in the middle?
From an engineering perspective, when you are holding the Torah scroll at the bottom, the gartel should be on the upper half because that is where it is needed more. You have the bottom under control but the top can tilt so it can also open or twist. Imagine trying to balance an up-side down broom on your hand, based on leverage, the higher (and further from your hand) you go, the less strength needed to straighten it.
In the Sefer Darchei Chaim in the note #65 on the bottom it says in the name of either the Divrei Chaim or his son the Shinever that it is done on the top third similar to Mezuza which is placed on the top third of the door.
Practicality. If left in the middle, when it is being carried and moved about, the gartel slips a little and descends (because of gravity), after which its function of keeping the scrolls together and tightly bound becomes severely diminished because it slips to the bottom. However, when placed in the top third, it does slip, and slips to the middle. In this case then its function is maintained, and the scrolls don't slip.