water weights 7.62 pounds per gallon, tub about 200 lbs, human 125 - 200, so that total divided by four is the weight each foot is holding up.
If this is a must, why not spread the weight evenly like installing a stained, sanded, treated plyboard like the flooring.
If this is not in the cards, then I would not do it.
The other alternative is to completely reinforce the under flooring by removing the top floor and do some structural re doing.
You could also place some blocks up under the tub where people cannot see to further dispurse the weight.
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