So, monster weight/mass is influenced by HD (weight is (HD * 10)^BME, where BME is a sort of base indication of how ferocious a monster may be for it's size).
In theory, then, the ability of a larger monster to save more effectively versus a "generic" dose of a poison is somewhat already there, though many monsters have better or worse saves than a Fighter of the same HD - it's not at all linear, not even within the same monster category.
The general gist, though, yea, one would expect a larger dose of poison to work better (or, at some point, kill the creature even if it's not meant to) because poison (generally) is based on biological and chemical functions. That'd include needing a larger dose to affect a larger creature.
In general, the supply cost of a creature quadruples every size category.
So, poisoning a griffon (Large) instead of a man (Medium) could take 4 doses to get the same effect, and underdosing the creature may give a bonus to the save (conversely, overdosing would give a penalty)
Highly conjecturally and assuming I didn't screw this up, one could make a guess as to what underdosing or overdosing may due to a saving throw. If we assume for the moment that dosing a creature 4 times causes 4 saves, and additionally it only takes one failure to cause the poison to take effect, we can basically calculate the save chance as (4d20 take lowest).
Dose a 4th level Fighter 4 times. That's 4 saves; and any failure gets him. The chance to save is (4d20 take lowest, at least 12+). The Fighter 4 saves vs poison on a 12+; a 45% chance to make it.
If he gets 4 chances to make the save, he's got only a 4% chance (45%^4). 3 chances is 9%, 2 chances is 20%.
That's how it works now, if you poison somebody 4 times at once.
If we map that to a single roll, that's about a -8, -7, or -5 to a single d20 roll, for four, three, and two doses, if we take that multiplicative chance as a flat chance.
Conversely, our Griffon fails a save on an 11-. That's a 55% chance. If any failure dooms the griffon, it's toast. Underdosing the griffon (3, 2 or 1 doses out of a 4 dose requirement) takes us to 30%, 16%, and 9% - or a +5, +8 or +9 on a single d20.
After about 6-7 doses off low or high the whole thing asymtotically approaches -9/+11, making it a 100% chance of success or failure. The table is different for every save value from F0 (15+) to F21 (1+) and is essentially the same sort of thing as 5E's Advantage mechanic - middling values benefit the most.
This'd probably make more sense if poison was "save or half" for whatever it's effect; then you could figure out a "save or nothing" value at the very low end of required dosages.