No one in Israel could put even a rebellious child to death without approval of the elders (Deut 21:21). Though Jepthah did indeed defeat the Amorites, that did not place him above the Law.
The weeping over virginity could well have been due to the fact that Jepthah's family line would cease, since his daughter was his only child.
There are commentators who do argue that Jepthah's daughter was indeed killed, so the idea can have some traction when reading the Bible. The very fact that the question comes up shows that it's not easily determined either way. Indeed, commentators also argue against death in this case and instead for consecration at the Tabernacle. Personally, after looking at both sides, I lean toward the latter. I'm not going to rail against anyone who wants to argue otherwise, nor make put-down remarks such as "Jesus, do you guys read much?".