Your hypotheses are pretty spot on. There is some observational bias, I think you are mostly looking at small molecules, as biologics typically have dosages on the order of grams. Small molecules are actually not too different in size, the molecular weight may range 10x between some of the smaller and some of the larger compounds (excluding outliers) which in biology is not that much of a difference considering that typical biological molecules range from the size of water or CO2 (18 and 44 Da) all the way to protein complexes that are >1MDa.

Next, the biology. Most drugs are given systemically which means they pretty much dilute themselves in blood which is pretty close to the same volume for most people. And of course, those drugs are designed to interact/interfere with typical biological processes which through evolution and for kinetic/thermodynamic reasons utilize a relatively narrow range of concentrations in the enzymes/receptors of the body. So a relatively close range of concentrations combined with almost constant volume and relatively close range of molecular weights yields close total dosage.

Lastly, there is pharmacokinetics. Every drug you take has three competing "things" it does. The effect you are looking for, the effect you are not looking for, and removal. The first two parts determine what's called a "therapeutic window". This is the range of concentrations where the intended effect is useful and the side effects are minimized. If you are above this range, the number and severity of side-effects will increase (again more or less back to basic thermodynamics) and if you are below, then your therapy will not be potent enough to have a considerable positive effect. This window can vary quite a bit, but at first approximation will center around the concentration of other similar molecules in the blood, which we already discussed above.

Then there is the clearance. If you are lucky enough to have a large therapeutic window, it may still not be advantageous to give lots of the drug. Most drugs at higher dosages are at first cleared by first-order kinetics whether through liver or kidney. This means that the more drug there is, the faster it is cleared. As concentration decreases, so does the clearance. So imagine you have a wonderful drug that is in the therapeutic window over a range of ~1000x concentration. That means if you give the max amount, you will be active for about 10 half-lives before the concentration decreases enough to no longer provide benefit (2^10~1000). Now you take that same drug and double its concentration. You have increased it's longevity by one half-life, meaning a 10% increase (11 half-lives compared to 10) from previous dosage in how long it stays effective. But to get that 10% you used 2x the drug. Not a great trade-off.

At the end of the day, each drug will have a dosage based on how effective it is at certain concentrations, which dosages minimize side-effects, what concentrations the formulation allows, and also what will lead to the highest rate of patients actually taking the drug (tons of people are working on ways to minimize insulin injections for example). There is some economics goin on as well, but not as much since the production cost for most drugs is small compared to the price.