Looking around I do see a high of 3.20 grams so your weight is high at 3.69 grams, but it does look quite real as well of course. Could just be a one off heavy flan was struck.
This is what I found too and why I had questions about the coin. From looking at online listings the average weight for the coin is about 2.7 grams. Therefore, this coin is almost 1/3 heavier than what you would expect. After some more research I found this article posted on academia.edu by Shawn Caza:
Weight, Fineness and Diameter Standards for Late Roman Bronze Coins - A Tutorialhttps://www.academia.edu/41222962/W...s_A_Tutorial
He lists the range for AE3 size coins as 1.5 - 4 grams. So Roman quality control was not all that precise and my coin is within this range.
Thank you louisvillekyshop for your input.