Bride price and dowry
That Proto-Indo-Europeans viewed a wife as part of her husband's family doesn't necessarily mean that the she would move to her husbands family (a practice called "virilocality"), it could be that it was expected of them to move somewhere for themselves ("neolocality").
However, if we assume virilocality, that kind of explains the practice of bride price, imagine that you have a daughter who helps around the house and field, but one day she's off to the her husband's family. That can seriously impact your own family's labour power, so financial recompense for loss of her labour power (and conversely, their gain of it) is a fair move in their eyes.
Even more complexly, imagine that you have a son of your own that you want to get a wife. After all, the procreative power of women is the base on which survival of family is based on. So when you marry off your daughter, you gain the financial means of helping your son get married in turn. All in all, wealth circulates around as marriages occur, and no clan or community is left bereft of women and to die a slow death by attrition as no one gets any babies.
Also, bride-price implies that having children is viewed positively and there isn’t too much scarcity in their locale. People will pay money (or in other goods) for something that will result in more family members under their roof. This is in contrast to a Dowry, in which the underlying idea is “Sorry about the fact that you’ll have more mouths to feed in a while as a result of my daughter. Have some money or livestock.”
Bride price is common in hoe farming cultures, dowry in plough farming cultures. Women commonly use the hoe, but usually don't plough because it takes a lot of upper body strength to drive a plough (even with the help of a draft animal). So in hoe farming cultures, a woman's agricultural labor is valuable; in a plough farming culture, she doesn't work outside the house, so she's another mouth to feed.
