Solution for different Wire sizes in one circuit
You should hire an electrician. You are going to start a fire or get shocked. But I will try to answer your question anyway.

Fuses and circuit breakers are generally governed by some type of code. I don't know what country you are in, but in the US, the national electric code (NEC) is generally the authoritative source. So based on wire diameter and insulation temperature rating, you chose a specific size of fuse or breaker.

The purpose of circuit breakers is to prevent the wire from getting too hot and burning up the insulation or starting a fire. However, you cannot protect 16 AWG wire with a 20 Amp fuse or breaker. In fact, I am not sure if the NEC allows you to use 16 AWG wire at all. The maximum fuse or breaker for 14AWG wire is 15A.

I also want to point out that putting two AC sources in series is a tricky business. The sources need to stay synchronized somehow. This makes me wonder whether what you are doing is a good idea in the first place. I hope you know what you are doing!