After a bit of searching, I found GSAP, and implemented it successfully (and smoother) than the jQuery animation I had previously created. It weighs in at around 80kb - so still not perfect (but that's with additional plugins to be able to use CSS selectors, if you animate an SVG you can probably omit the 60kb required file).
I'm wondering if there are any other great options available.
The best options:
Do not rely on jQuery!
Either does not rely on CSS3 Keyframes or has a fallback for when CSS3 Keyframes are not available (for backwards compatibility)
Has minimal file-size and requires few or no other files to be included
Is not too complicated to learn! (either good documentation, or familiar/simple syntax - I don't want to spend days constructing a simple animation)
I'm not interested in Flash at all.