This is an interesting question. I’ll be honest, if the breasts hurt every time they got hit then women would be doubling over every time they ran into a wall and bras would contain much more protection and padding than they do so women could get through their normal everyday lives. Since they don’t, the answer is: not that much.
The first notion to dismiss is that a woman getting punched or kicked in the chest is anywhere near as physically painful as a knee to the groin. Getting kneed in the groin hurts so much because of the high number of nerve endings there, since both men and women have those with a similar level of easy access. Still, the groin is a fairly well protected area as regions of the body go, it’s protected by the legs when standing and sitting and can be easily hidden by curling up into a ball. The breasts are just out there and despite their importance for feeding babies and arousing sexual pleasure, if they were extremely debilitating the body would protect them better.
Now, if you’re not wearing padding or some kind of binding (like a sports bra, regular bra, or a breast band) it can be somewhat painful to be hit there. Just as it would be in any region that’s protected by a fair amount of fat. A female character will probably be wearing some sort of binding or bra just for general comfort. A sports bra binds the breasts down very tightly because it’s specifically designed to inhibit movement, but any type of binding that essentially crushes the breasts together will work. This provides some measure of protection, but it’s important to remember that bras are designed for comfort and the breasts jiggling and jostling around while you’re moving can be anywhere from annoying to marginally painful. So, the woman will attempt to limit their movement as much as she can, but not because it hurts to get hit there.
The best way to hurt someone on their chest region (assuming they’re not striking to the breast bone or between the breasts for the heart) is twisting the nipple (this will work for most men too), but because of the bra, getting to the nipple through the clothes would be difficult. The pain also won’t last long enough to be debilitating.
I’ll be honest, there isn’t much reason to strike to the chest as opposed to the stomach or the neck. It’s something of an intervening space that’s well protected by both muscle and bone. A woman’s breasts don’t change that equation much, other than providing the chest with even more protection than it had before and a nice guiding line for where to drive a knife. (Which is why you should never have your characters wear boob plate.)
On the subject of small breasts: I’m not a doctor, so don’t expect me to give you a full biological breakdown for how the breasts work. But here’s a simple answer: the breasts contain the mammary glands, those glands are protected by fatty tissue. Essentially, a large portion of what decides the breast size is fat. When the body is looking for stuff to eat while a workout is burning up it’s energy, it starts chowing down on the body’s fat. Any normal kind of sport activity will shrink breast size to smaller than it was before if they are expending energy regularly. I’ve had plenty of female students and workout partners complain about their breasts getting smaller, this can be incredibly disheartening for those women who start working out as a means of increasing their attractiveness.
So, yes, they do. Though, the information I’m giving you is if the woman in question hasn’t had children. If she has, then her biological makeup will change.
Breast size has more to do with how annoying dealing with them in training is as opposed to how much hitting them hurts. But look at it this way: more fat = more protection, less fat = less protection and closer to the muscles. It’ll probably hurt more, but not enough for it to really matter.
Think about it this way: if it was debilitating or even just hurt a lot (enough to provide a useful advantage) for a woman to be hit in the breasts, people would do it more often. The myth about the testicles versus the clitoris exists because it’s so much more difficult for an untrained fighter to knee a woman there as opposed to men. Men wear cups for a reason, the testicles are ridiculously easy to unintentionally (or intentionally) clip.
I hope that answers your question,