This is a whirlpool tub that is the standard size of regular tub except a little deeper so I think you are probably allright if your floor would support a regular tub. With one that size, you will only have 35 (more likely about 35) to 50 gals of water at the most. Put a body (or two if you like to have fun) in it and it displaces the water so you use less water. You also can't get too full because of the overflow and splashing. So basically you have a standard weight tub.
Assuming 16" centers and joists large enough to support the 2nd floor and a tub, you should be ok. The tub base and the mortar base you set it in will help spread the weight over the floor. If concerned then sister in additional joists along side of the other ones since it is open. If still concerned, apply the same size joist as bridging between the joists directly under the middle of the tub for added support if you want. Err on the side of overkill (my motto) since it would be expensive to fix later.
I basically fill mine up to above the jets and by the time I get in, it is almost full. On ones I have put in, I invert the overflow so it fills in from the top instead of the bottom to get 2 or 3" more in depth. Sometimes cutting a rubber gasket like a horseshoe and putting it behind the overflow helps keep the water going in at the top of the overflow. I think they cut the hole to low on most of them. I don't recommend plugging the overflow cause some kids or someone will have an accident. While using it, stuff a washrag in the hole if you want another inch or two.