This is harder to classify than you might expect. The first reason is regional access. In Germany, BL stores have access to one or more gray sources (or at least sources they play close to the vest), and you have multiple stores competing with 1+ million parts. ChromeBricks has about 5.8m parts right now. Outside of Germany, there is no parts source available to sellers, so a large store is probably 500k+. The critical mass to sustain regular orders seems to be about 50-60k, so I'd say that 50k-500k are "medium" sized stores. 5k-50k are "small, but serious stores". Less than 5k are usually hobby sellers trying to unload excess parts from their collections or make a quick buck.
The second issue is lot quality and lot diversity. Because there is no easy source (excluding Germany), medium and large stores build their inventories up in different ways. Some stores are aggressive parters, buying 20+ copies of a set at a time and parting them in. The best example of this is PBD which was "going out of business" for a year and liquidating but changed their mind recently. The challenge with this model is that the demand for specific parts such as basic 1x4 bricks does not match the distribution of those parts in sets. So your store ends up holding 20x lime wedges for years while the 20x blue 1x4's will sell within a week. Over time, this leads to huge inventories (PBD is 2.3m) but little of it is liquid. Other stores have old recycler stock that is lingering. An example of this is Lonely Brick which has 1.1m parts, but 20% of that number is in 4 lots. Anyone need 70,000 reddish brown 1x1 cones? Another band of sellers are PaB wall miners. The majority of their store inventory comes from buying PaB cases from LBR stores (although Lego is really trying to weed this out with changes to the policy this year). This allows them to build up decent inventory quantities, but the variety of lots available is the same across many stores, so the price competition on those lots can be fierce (read: no margin). Every store finds their niche, which makes it such a fascinating marketplace. We try to use a balance of methods that keeps our inventory diversified and attractive to buyers. We've found that its really hard for us to keep more than 1m parts in inventory because they turn over faster than we can restock.
An alternate way of looking at BL store sizes is to analyze selling feedback volumes for the past month. You can see the sellers ranked by feedback here. "Large" stores are getting 200+ feedback per month, which equates to roughly about 300 orders per month. "Medium" would be 100-200. "Small" would be 20-100. "Hobby" would be less than 20. When you put the inventory number side by side with the order volume number, it sheds more light. For example, Sir Troy has 1m parts but only 50 feedbacks posted in the last month, meaning that his store is not very active despite the parts count.
If you end up publishing data on this, I'd be very interested in reading the findings. -Jason