It's all over the place. The LoI guide indeed says the Morris family split off from the Belmonts between Trevor and Christopher, but one version of the official time claims they split off after Richter, and there's also Japanese material from around the time of Bloodlines' release that claims John Morris is a descendant of Simon.
Okay, this line of thought intrigued me, so I dug out my old genealogy notes from a while back, and started a couple more hours of digging because can't stop won't stop.
So, given that in America, the concept of "old families" generally means well established
since the 1700's to the early 1800's, it would be kind of weird (at least at first glance) to have the largely American Morris clan crop up a full 200-300 years earlier than that. Based on that assumption, I'd peg their historic emergence probably around Richter's time, perhaps a little later. It fits in with the American perception and timeline of Old Families, and since the Belmonts couldn't use the whip after/because of Richter, I'd say the integration of Belmont blood into the Morris family may have effectively served as a sort of genealogical Plan B.
However, it's entirely possible that the Belmonts married off a daughter or a lesser/illegitimate son to the ancestors of the Morris family, which, based on the history of the surname, also makes sense -- it's been around since the mid-1200's, and, like Belmont, derives from in and around Normandy, in France.
So, the Morris family may have been linked to the Belmonts around the late 15th or early 16th century as posited by the LoI guide, back when they were (probably) known as the
St. Maurice family, which, in the real world, was apparently some manner of French nobility that became "Morris" after emigrating to England. Becoming English explains how the Morris family arrives in America: they were very likely colonists in the early days before the American Revolution, and likely headed west to Texas (where we later find Quincy is from) with the large push of Westward Expansion, which, by Quincy's time, had made enough new fortune in the Ranching business to be able to rub shoulders with the English elite and be a serious contender for the hand of Lucy Westenra in marriage. It's worth noting that the Victorian era London Elite is generally considered to be
slightly more snobbish and exclusive than the New York City Elite, which if you know anything about the New York City Elite from the same period (Winthrops, Hearsts, Carnegies, etc.), is saying
quite a lot. If you've made it to the point where you can rub shoulders and compete with
them, you've damn well made it big.
Props to Iga, he also got Leon's timeline as an early Belmont
spot-on -- the earliest records of Belmont as a family name are from around 1066, so it's highly likely that, assuming Castlevania's pre-LoI history closely resembles ours, Leon is either a first or second generation bearer of the name. The real-life Belmont clan was apparently related by some degree to William the Conqueror, which would explain Leon's nobility in-universe. Furthermore, Leon was a very popular name in France for centuries, his knightly colors are very French in design and color choice, and his features are as close to French as you can get with Ayami Kojima's art style... so I'm gonna go ahead and say he's probably French. The evidence does seem to fit this assertion.
We can also see a pattern in the countries associated with given names of various Belmonts: Leon (French), Ralph (Norman-French)/Trevor (British), Christopher (mostly French, but crops up basically everywhere), Soleiyu (French), Simon (like Christopher, basically everywhere in Christian Europe), Juste (French), and Richter (German). We can fairly determine that the family is largely a French one, with occasional external branches chiming in some influence.
I find this last bit particularly interesting because the geography of Castlevania isn't often discussed by the series, with only a few games having their specific settings stated beyond just "The Castle", but naming patterns like this can give a lot of background details about the surprisingly grand scope of the mythology.
It's also an interesting story: a French clan loses their noble title, heads pretty far east to Wallachia (predators tend to follow their prey and Wallachia def seems to have a super bad vampire infestation), settles, regains some manner of title almost 400 years later (thanks to the whole "saving the world from Dracula" deal), and then, after marrying with another noble clan, spreads back out across Europe and has links as far away as the New World, where they are still active over 600 years later.
Goddamn I love studying names and history.
EDIT & Noncanon bonus! Sonia is a predominantly French spelling of the name (as opposed to the Russian and Scandiavian "Sonya" and "Sonja" respectively), and she shares a lot of Leon's more obvious Western European phenotypes, though a lot of the precise details are lost with the low-budget anime art style employed in Legends. So even if LoI and SOTN never happened, the Belmonts seem to remain a predominantly French clan. So I thought that was neat.