To put it crudely: the earlier you start, the longer you can go.

First is the matter of producing heirs. Medieval maternal mortality was high, but not catastrophic. Schofield's and, separatly, Herlihy/Klapisch-Zuber's figures of 1% per birth in the countryside, 1-1.5% in cities, with a slight uptick in mortality for younger and older women give what scholars accept as a lifetime risk of 5-10%. The younger noble wives started trying to have children, the more likely they were to produce male heirs who would themselves survive to adulthood.

Second, elite marriages (upper-class urban gentry, nobility) marriages in the Middle Ages were political tools. In addition to the production of offspring whose inheritance could unite different regions, a marriage provided solid ground for long-term diplomacy: whether this entailed the new wife bringing with her servants or an entourage, or simply visits from "concerned relatives."

Although the idea of remarriage was frequently discouraged in some clerical writings, with the idea that widows should retire to a life of piety with Christ as their spouse, in practice remarriage was widely accepted from the 13th century onward. On one level, remarriages allowed families to make new alliances. In Renaissance Italian cities, for example, it was basically a startover: widows returned to their father's household and had a new alliance made for them. (There are a few cases in 15th century Italy of lower class widows staying as independent heads of household, but this was basically non-existent for the upper classes). Sadly, they had to leave any children behind with their deceased husband's family, although this likely provided some ongoing benefits of the former marriage alliance. It would not surprise me if second marriages in Renaissance Italy generally required a larger dowry than first marriages--we know fathers had to pay more to ensure their "too old" daughters got a good match (and consequently tended to lie about their ages!), so it wouldn't surprise me.

Among noble and especially royal widows, remarriage was its own type of political weapon. The Parliament of England tried to prevent Catherine of Valois (immortalized in Shakespeare's Henry V) from remarrying after the king's death precisely for this reason. She probably didn't listen--we don't have official records of a marriage, but the idea of a clandestine marriage being valid but illicit still existed in the 15th century--but her relationship with Owen Tudor produced future King Henry VII and launched the in/famous dynasty.

Or, in 15th century Hungary, there is the spectacular case of Queen Elisabeth (not the 13th century saint). Although she was the daughter of the previous king, the crown of Hungarian monarch had passed only to her husband Albert. He died leaving her with two daughters but pregnant. The Hungarian nobles pressured Elisabeth to remarry, so they could crown her new husband king (as Hungary was under military threat at the time). Elisabeth held out. When the baby turned out to be a boy, she not only continued to refuse remarriage, she plotted with a handmaiden to steal the actual, physical Hungarian crown to arrange a coronation ceremony for her son. Who became known as Ladislaus the Posthumous, yup.

Marriage and motherhood were careers for aristocratic medieval women. The earlier they started, the longer they had to make themselves as successful as possible.