Franklin2 nailed it. It was one of the attempts to improve emissions. The O2 sensor signal controlled the solenoid, giving a crude closed-loop fuel control.
The Weber carb is widely used in Europe and there is a lot of info on tuning on the internet. Franklin2 is also correct about the adjustability. There are air jets (they call them air correctors), emulsion tubes that operate on dark magic that nobody seems to understand, main fuel jets, idle fuel jets, idle air corrector orifice (pressed in, not easily changed), and I'm probably missing other adjustment points. You can't change more than one thing at a time or you'll just chase your tail forever, so it gets time consuming changing an item, then testing, then repeat.
There's a unique procedure to setting up idle that is detailed in manuals and forums on the internet. Beyond that there isn't a ton of guidelines for tuning. I found a website, I think it was for a company that does tuning in Europe, that kind of laid out the trial and error process and order that things should be dialed in but I can't find it at the moment. Different components of the fuel/air controls in the carb have larger or smaller effects on final AFR depending on throttle position and engine speed.
The carb, timing curve, PCV, and engine characteristics all interact to give overall performance. I used a wideband O2 and vacuum gauge to help with tuning. Sometimes things outside of the carb present like problems with the carb. I chased my tail with a tip-in stumble for a long time until I finally figured out it had to do with the PCV. The PCV opened just before the carb started to draw enough fuel. Adding enough fuel or removing air caused it to be too rich in other areas. Tuning so cruise and accel AFR was where I wanted it made the stumble worse. If I removed the PCV from the intake, I could tune out the stumble. I didn't want to lose the PCV, however, and experimented with a few different PCV valves until I found one that worked well enough and that's when I called it good. I eventually got tired of taking the air horn of repeatedly to change jets and air correctors.
Maybe the actual bona fide Weber would work better, but I was able to get my Holley copy for $20 plus a $50 rebuild kit so it was a lot less invested. A proper intake would also probably help a lot. There's quite a bit of restriction as the adapter goes from 2 to 1 barrel.
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