You will be able to take for 16 day trip keep three formal night outfits, dressy shoes to match and a different outfit each day.
Airlines allow restrictions for luggage taken in just a small 21 inch carry on. 21lb (9.53kg) exceeds many international airline carry-on weight restrictions in 2017. You are allowed 100ml bottles.
If you change airlines the lower limit usually applies so best to check and take.

This is an amazing technique I found form our friend’s comments use plastic foil for each garment to minimize wrinkling in clothes.
You can put some things into shoes to use space like socks.
If you unpack every day. But if you travel for a week for work & are in a different hotel every night or two, this will be too much work.

Divide packing and folding in parts. Packing cubes are good for casual trips, this method is much better for packing nice / business clothes.
Use space saver bags. Fit 7 complete outfits of warm clothes.
For winter vacation you can pack the same method regardless of weather and adjust layers according to temperature changes.
3 layers, and then Jacket are typical keep packing light, it is good to have Omni-Heat thermal reflective clothing. They are light in weight.:)