Kayla is one of the most soap opera influenced names in the USA, being clearly linked to the character
Kayla Brady on "Days of Our Lives". If you look at the popularity curve for
Kayla, you will see that it starts up in 1982, peaks in 1983, then actually recedes a bit in 1984 and 1985 before taking off in a big boom in 1986. And the character of
Kayla Brady was introduced on "Days of Our Lives" in 1982, left the show in 1983, and returned to the show (played by a different actress) in 1986, following that popularity curve exactly.
However, so far I can't find a specific reason for
Kaylee's upswing other than parents wanting to create a "different but not too different" version of
Kayla.