Unfortunately, it is impossible to obtain Kantonian Weezing without having bought the Expansion pass. An exception to this is if you would transfer Weezing from an earlier game to SwSh. Like Alphacelestius said, evolving a Pokémon will still have the final result be its native form, not considering generation 7. If you have the Expansion Pass though, you'll need to have captured Galarian Weezing first. You have to look for a NPC called 'Regina.' Her possible locations are:
- Brawlers' Cave,
- Challenge Beach,
- Challenge Road,
- Courageous Cavern,
- Fields of Honor,
- Honeycalm Island,
- Insular Sea,
- Potbottom Desert,
- Soothing Wetlands,
- Stepping-Stone Sea,
- Training Lowlands,
- Workout Sea
The only way to get Kantonian Weezing is to trade your Galarian Weezing with her. She asks for random Pokémon to trade for, which means that you should be prepared for if she asks for another Pokémon than Weezing. According to this reddit thread, If you have finished the Isle of Armor Pokédex you can buy Apricorns from a lady with a blue shirt, this will change Regina's location. It's unsure if this also changes her Pokémon.
Source: This, this and this :P