Yes, there’s been research. There is no evidence that wearing a bra helps prevent sagging and maintain the shape of the breast.
Look at pictures of any NSFW: traditionally toplesswomen, who usually live lives full of physical labor. There is a variety of breast sizes, some are plenty big proportionately.** NSFW**: Zulu women (more), Embera women, Afar women, Dinka woman. Plenty of these women could have cleavage to rival Jennifer Tilly, in the right bra. Many of the young women have round, perky boobs.
Americans (and Brits) wear a much larger bra size on average than much of the world, but that’s mostly due to the fact that we are bigger all over. A women who usually wears a 36DD looks very different from one who wears a 32DD (who often gets called ‘small’), but proportionate to their body size they have the same amount of boob.
All boobs change throughout life - aging and later hormonal changes have an effect, but by far the biggest changes come with pregnancy. There is again no evidence that breastfeeding, or how long you do it, changes the appearance of your breasts - all of the changes to the breast have been made by two days after birth. As I’ve always understood it, and has been recently correbated by all my friends having babies, during pregnancy you see a large increase in the actual ‘mammary glands’ within the breasts. The helps increase your overall size, and might stretch the skin of the breasts. After you’re done breastfeeding, or if you don’t breastfeed at all, the milk-producing tissue shrinks back down - which often leads to a ‘deflated’ appearance, which may or may not go away as the skin tightens back up and fat up the space left by the actual breast tissue. The more pregnancies, the more likely it is that you won’t see a return of your former fullness, and I’ve always assumed that is why older indigenous women have breasts much more deflated in appearance than any of the older American women I’ve seen topless. Most of them have no access to birth control.
Now that I’ve been reading up on it - I find it very interesting that there are almost no cultures where habitual female nudity of the buttocks, genitals, and upper thighs is permitted, but that hundreds and hundreds of cultures in the Americas, Asia, Africa, Australia, and the Pacific islands did (often until very recently - say 1930s-50s when ‘decency’ laws were enacted under colonial rule) or still do have traditional garb that leaves the female breasts totally exposed. I think Christianity and Islam are responsible for a degree of fetishization breasts have seldom seen before.