If your 20 grams is +- half a gram (as one might assume if your scale will show 19, 20, or 21 but no fractions), at worst your error will be about 2.5% (half a gram heavy or light). You'll normally use 10 ml of 1% solution in a developer, which would mean your intended 0.1 g might be anywhere between 2.5 mg more or 2.5 mg less than intended. I doubt it's enough difference to worry about.
You might, however, consider getting a better scale -- I've got one that cost about $40 that reads in 0.1 g up to 1 kg and then full grams to 3 kg -- and this is after subtracting any tare, so I can still see (for the kitchen one that prompted me to get a second for the darkroom) 0.1g accuracy for my 40 g of coffee grounds with the empty carafe and dripper cone with wet filter on the scale, more than 500 g of tare -- and *still* see tenths when I've tared the grounds and added 800 g of hot water in brewing my coffee (total weight on the scale well over 1 kg, but still reading out in 0.1 g).
Not that this would be a good practice (because what if you overshoot?) but with this Kitchentour coffee brewing scale you could put a 1000 ml beaker filled with water on the scale, hit tare (to subtract the weight of the glass and water) and still see tenths of a gram as you add your benzotriazole to the water.
I can't tell you the shelf life of the BZT solution. I've only used BZT in my darkroom once, and I did so by adding a single tablet of Kodak Anti-Fog No. 1 to a liter of borax-accelerated D-23 made up specifically for sixty-five-plus year old found film.
