I was looking at some maps and this trend seems to be all over the world. I certainly have some guesses, such as expansion stemming from the "easier side" to use, but has this been studied at all?
Though small trading and supply villages occur with only river access, large cities grow where some other form of transport (wagon road or railroad) comes to the river. Not only does that convergence of transport make it the port of choice for the region, but the transfer from one mode of transport to another turns the settlement into an entrepôt. Since you already have laborers moving the cargo around, it’s a good place to set up a mill or factory that adds value to the raw materials, or a warehouse that turns bulk shipments into higher-value retail shipments.
Of course, other factors also come into play. The presence of a royal court, as at Dresden, Lisbon, Istanbul, or Bangkok, will attract development to one side of a river, as did the defensive walls that once encircled many European cities. In addition, one bank of a river may be marshy or prone to flooding, while the other enjoys a better situation for citybuilding.
Eventually, access to the big city prompts development on the other side of the river, as seen in St. Louis, Cologne, Yangon, New Orleans, Montreal, Shanghai. Cities on modest, easily bridged, rivers tend not to be so lopsided, as with Paris and Moscow. The same is true for cities that grew large in the 19th or 20th century, such as Seoul or Portland, when even large rivers could more easily be spanned.