You don't need 16-bit. Highly unlikely. Any 8-bit controller can do 16-bit math, just not AS fast as a 16-bit core. Servo controller doesn't need all that "fast".
PIC18F1320... powerful, probably more so than you need. ~$3.25 in singles. 6mm x 6mm QFN28 package. That's not only small, but light. It's a much thinner package than leaded SMD.
Basically for small/light, look at QFN pkgs. Most controllers have a QFN variant now, actually. A QFN16 will be slightly smaller than a QFN28.
Not as hard to mount as you might imagine. Flux, solder paste. Heat gun. Turn the heat gun down or hold it back for a preheat needed to boil the solvent out of the solder paste. It'll stop bubbling. Then turn the heat gun up and bring it closer, see the solder turn silver, count to like 3-5 sec, pull it back. Done. Check pins with a pocket microscope. In general, the package should have self-aligned exactly. Generally if it IS off, it'll be off by "a lot" and you'll see it.