Your 125 gallon has a footprint of 72" x 18" covering 9 square feet. Your tank holds about 1,037.5 lbs of water. Your tank plus stand probably weighs about 250 or so pounds. This will result in a load of 1287.5 over 9 square feet resulting in 150 lbs of load per foot. Maybe 1400 with rock.
Modern residential building code in the United States calls for 30 psf live load for sleeping rooms and 40 psf live load for non sleeping rooms.
You can multiply the area of the room by 40 psf or 30 psf depending on your situation to get an idea of the capacity of the room. The room contains you, your furniture, and your new aquarium.
Obviously the situation is better on the edges of the room, next to load bearing walls, perpendicular to the joists below. The design loads above assume the weight is going to uniform which it won't.