If Frank is correct with the 42 gallons to overflow and water weighs 8.34 lbs/gallon. That gives us a max of 350lbs. for the water alone. If the standard tub covers 12.5 sq. ft., that gives us a live load of 28 psf. Floor has to be designed for 40psf minimum. Add a 150 pound person would equal 40psf. Then throw some actual logic into the conversation....my kids are the only ones to in my house that take a bath. We don't even have a tub in our master. It's doubtful a person will ever fill the tub to the overflow line and then climb in. The other this is this only matters if the floor joist is at max span. We're talking basic, minimum code.
I'm really only watching this if there is a large, two-person jet tub in the master bathroom.