Japan in September
 

Just now starting to plan for 2020 with another couple. Trying to get a suitable month for the 4 of us. Any advice as far as traveling the first 2 weeks of September. Otherwise will try for the first 2 weeks in October which I think is preferable.

Here's a good resource to help you decide, and BTW, it's an excellent resource for planning a trip to Japan in general.
https://www.japan-guide.com/e/e2273.html

Early september is still during typhoon season. I'd go in October.

My last trip was during the first three weeks in September. It was rainy during several days, and the humidity makes it difficult to walk around. The rain was heavy at times, enough to make the usual walking that I like to do very unpleasant. On dry days, the humidity made me sluggish. I'm not sure about October, but if the predictions are for less humidity and rain, then that sounds better.

First I think it depends upon where you are planning to go. This year we were mostly in Honshu the last 2 weeks of September and the first 3 weeks of October. Overall we had nice weather.
There wasn't a lot of rain with the exception of 2 typhoons. Fortunately, we were not in the path of either and had no impact from the major one Hagibis which struck ~Oct 12. We had heavy rain and wind from the other, Mitag in early Oct. It was more of a tropical storm by the time it reached where we were. That particular day we were driving down the coast of the Sea of Japan. Obviously you don't want to be there during a typhoon, but I will add the people we talk to who were in the path of either storm said it just meant staying inside their hotel for one day, so it didn't impact a major portion of their trip.

I've stayed in Tokyo and Chiba during September, it's typhoon season so expect a lot of rain. It's starting to get chilly in the first 2 weeks of October since it's the start of the Fall season. Weather aside, I think October would be more eventful, expect Halloween and Fall decorations on landmarks and tourist attractions like Tokyo Skytree, Tokyo Disneyland and DisneySea, and even Universal Studio.