Let's say we have two continuous variables, $a$ and $b$, both being positive with $a\leq b$ and the outcome in a regression is their ratio. The typical solution is beta regression (see for example here). However, something started to bother me. If we divide them and apply a regression for the proportion, then $1/5$ will be the exact same as $1000/5000$... while my intuition is that they shouldn't be identical, as in the latter case we are much more sure that the proportion is $0.2$ than in the former (the sampling variability is much smaller).
Isn't it a problem for beta regression? Or I overlook something...?