I remember reading that four of the seven dwarf families resided in the Orocarni. Does this mean that dwarves were more common in the East than the West?
It's possible, yes.
From the essay Of Dwarves and Men, published in History of Middle-earth 12, the connection between the clans and their original homes looks as follows:
- The Firebeards: in the Blue mountains
- The Broadbeams: in the Blue mountains
- The Longbeards: Mount Gundabad
- The Ironfists: somewhere in the East
- The Stiffbeards: somewhere in the East
- The Blacklocks: somewhere in the East
- The Stonefoots: somewhere in the East
Although there were seven clans there were only four awakening places: the Blue Mountains, Gundabad, and two in the East. The awakening places in the East were unnamed; the most Tolkien says about this is (from the same essay):
The other two places were eastward, at distances as great or greater than that between the Blue Mountains and Gundabad...
If we assume that these were in the Orocarni (which is by no means certain: Tolkien doesn't say "yes", he doesn't say "no" either), this also provides a hint about the geographical extent of Middle-earth.
Unfortunately Tolkien doesn't go into any detail about the relative populations of each clan, so we can't say anything other than that there were originally more clans in the East.
I think Tolkien was hedging his bets with the dwarves when it came to 'canon'... at one point (I think it's in 'the people of middle earth' or 'the making of middle earth'...I confess, I do not have book XII), he began with the idea that because the Naugrim were not children of Iluvatar (they sprung from Aule the Smith) they did not have power to create (something like "therefore, they could not make anything of beauty, except in imitation of the elves") ... on the other hand, he gives the dwarves of The Hobbit, and Gimli even more so, distinct 'human' qualities (and even suggests that Gimli, by the grace of Galadriel and friendship with Legolas sailed to Valinor).
I suspect Tolkien was torn on his role for dwarves between the literary and the legendarium...and his concept of their role changed over 40 years.
Of interest is that most of the names of the dwarves in The Hobbit were derived from Nordic mythology. perhaps he had plans for eventually detailing the Naugrim and their languages, their sundering, etc., as he has done with the elves. Maybe as an exercise in backward-extrapolating the afro-asiatic language tree?... But like the blue wizards, who disappeared in the east...their fate is a mystery.