Cuteness is an emotion we feel towards things we want to protect. It is natures way of making you want to protect the weaker members of your species. Fur example, humans are hard wired to find babies cute, because they can't protect themselves. Men are hard wired to find women cute because men are evolved to be protectors of the tribe.
I believe women experience "cuteness" more acutely with children and small creatures (which are found to be cute due to their similarity to babies) while men experience it more with adult women. This makes sense as evolutionarily women are caretakers and the ones who raise the young, so their biological drive makes them want to protect children (hence why women make up the vast majority of teachers because they are driven towards child rearing).
I am not sure it's fully accurate to say women experience cuteness "more" than men, it's just that fur men it's across a broader group, being both women and children, while fur women it's mostly children. So fur women the cuteness they feel is directed towards a smaller group and it seems to be higher as a result.