Keeping your Macbook connected to a charger is no problem. It wouldn't make much sense to leave it unplugged and drain the battery every time just to recharge it again and unplug again. Especially if you are doing heavy tasks on it which drain the battery even quicker.
Cycle Counts will remain low if you just let it plugged in and you can get away if gaining only one cycle per one/two week period. If your Air is older (2015ish or older) you should however once a month drain it and recharge it so the battery meter remains somewhat accurate in measuring the actual remaining run-time. On newer models I believe macOS does this automatically and uses the battery from time to time even with the power adapter connected.
I unplug my 2013 MacBook Pro at night when I go to bed and do a full discharge every month. This is especially important if the computer has only been used on a desk, was plugged in almost all the time and not really used on battery power for some time.
The old battery of my Macbook had swollen up, and while I don't think that it was the result of me leaving it plugged in most of the time, or maybe it was just an overall defect, but I think it was rather the result of excessive heat that is building up in the chassis because of the poor software engineering regarding how the fans are controlled (they only kick in when the Computer already is very hot in favor of keeping the device operating quietly) which I think is total rubbish. I'd rather have a cool computer that does make slight fan noise than an overheating one. I wouldn't run any Mac without MacsFanControl anymore. If you don't have it installed, I highly recommend it.