Is it possible to know why an airline operates specific equipment on certain routes?
There are many factors, but you can often predict what class of plane will be used for a particular route by the distance and demand.

For smaller cities, they want to fill the planes, but they also need several flights per day to cover the fixed costs of serving that airport (and make things convenient for customers), so it's often better to have a commuter jet bouncing to the nearest hub and back several times per day day than one large plane that carries an entire day's worth of passengers in one shot.  For larger non-hub cities, they'll do roughly the same thing but with mid-size planes.

Between hubs, they'll run the largest narrow-bodies to connect all the various small cities not served by a common hubs, plus hubs themselves tend to be large cities with plenty of native demand too.

For international, they'll run wide-bodies because they need higher fuel capacity, and there's rarely a convenient time for customers due to the long flight times combined with crossing several time zones, so you might as well pack them into as few planes as possible.

Notably, some carriers fly several different types, each optimized for specific route types, while others fly just a few types (or even just one) because that makes maintenance, pilot training and fleet scheduling easier--but may limit what kinds of routes they can fly profitably.  When airlines merge, they'll usually have similar fleets--and in cases where they don't, they'll quickly start dumping types they don't like and replacing them with types they do.