Water weighs about 8#/gallon. A residential floor is designed to hold typically 40#/ft2. This includes the subfloor and floor, if present. A typical tub would not exceed those loads. Check how many gallons the tub holds, add the weight of the tub and the person sitting in it and divide by the say 15 square feet (assuming a 36x60" tub) and see what you get for a load.