What is the etymology of "cavalier"?

In the English Civil War (1642-1651), the Cavaliers were the supporters of the King, opposed to the Roundheads, who supported Parliament. Cavaliers wore their hair long and dressed in conspicuous finery; Roundheads cut their hair short (hence the name) and dressed very plainly.

The Roundheads won that war, and I suspect that the pejorative sense of "cavalier" arose as a result, especially since your first citation seems to have appeared around the end of the war.

wiktionary has the following etymology for the English word:

cavalier 1589, from Middle French cavalier 'horseman',
[1] from Old Italian cavaliere (“mounted soldier, knight”),
[2] from Old Provençal cavalier, from Late Latin caballārius (“horseman”), from Latin caballus (“horse”)

The first sense of cavalier is that of horseman and especially of horse-soldier or knight. These were troubled times in many countries and being a cavalier most of the time meant being armed.

Cavaliers had many opportunities to make use of their arms (fencing spades and later pistols). However, to avoid resorting to these extremities cavaliers needed to intimidate their potential opponent and to do so cultivated the art of inspiring fear. One way of doing so was to show disdain and self confidence.

This trait of character was not limited to roads or roadside inns but was also to be expected in society. Cavaliers were expected to be very assertive against other male aristocrats as a way of upholding their rank whilst also very gallant with women (hence the other - opposite - sense of gallant present in cavalier-servant).