Can anyone confirm what is considered standard practice for the number of scoops of beans for a normal cup of coffee (non americano, non-espresso beans)?
The are both ill-defined terms. A better measure is brew ratio, which describes the water to coffee ratio in mass units. On handground.com, there are a lot of recipes for AeroPress with brew ratios ranging from 17:1 at the weakest up to 8:1 at the strongest.
I'd suggest starting somewhere in the middle and adjusting based on the results. Since you're already getting a weak cup, the next step should have a slightly lower brew ratio.
You can either switch to mass units (grams or Imperial units with a simple kitchen scale work fine). The benefits of weight units are twofold:
They're more precise. Most kitchen scales are accurate to the gram or even a tenth of a gram. With scoops, you may need to use something like a little bit less than a full scoop and you'll have difficulty reproducing that exactly, even more so when you want to adjust a little bit.
The units translate to different coffees as well. Suppose you have a coffee with a different roast level, then its density may also vary. As such, a volumetric scoop of one coffee contain more or less coffee than a different variety of coffee. This is more of a factor when working with whole beans, but if you buy pre-ground the grind size will also have an impact when using volumetric scoops.
So I'd suggest switching to mass units and keeping track of adjustments and taste. If you don't like to get into the whole ratio thing, you can just fix the water content and increase the amount of coffee to get a stronger cup. The only time when you need to change the amount of water is when you want to adjust how much liquid you get in your final cup.