Could this also express "You are getting tall," something I have often said to a growing child?
Yes, it's often said like that, but in Indonesian the meaning is more than that.
It's an adverb meaning "more (and more)".
"makin" = "semakin" = "more", "more and more", "increasingly".
Kamu semakin tinggi = You're getting taller (and taller).
Kamu semakin gemuk = You're getting fatter (and fatter).
Kamu semakin cantik = You're getting more and more beautiful.
Kamu semakin dekat = You're getting closer (and closer).
Kamu semakin jauh = You're getting further (and further) away.
"increasingly" (tall, fat, beautiful, close, far) could also be used in the above examples.