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So, my question is:
Is there any biological barrier that would prevent a species of primate to develop, in a matter of few million years, extreme sexual dimorphism, where females would be size of a large gorilla while males would be size of a smaller chimpanzee?
While there are species of fish, insects, etc to have drastic sex differences, I don't think I heard of an example where such massive change would exist in more... "complex" organisms.
Is there any biological barrier that would prevent a species of primate to develop, in a matter of few million years, extreme sexual dimorphism, where females would be size of a large gorilla while males would be size of a smaller chimpanzee?
No, for mammals it is usually that males are dominators...but the contrary can happen as seen in hyenas.
It's also about sexual selection too.
To explain sexual selection I will give you example of Emo/goth girls. Some guys think they are ugly and ridiculous while others think they are incredibly beautiful.
Therefore the emo girls will go with boys who like emo girls. And normal girls will go with boys who like normal girls. Eventually you will see two different species emerging.
That's how sexual dimorphism caused by sexual selection happens....Peacocks evolved from birds with normal tails, but some females of their species were attracted to males with big tails, some weren't..they eventually split in different species.
Why do we have so many male dominant species? because girls seem to enjoy males which are stronger than them in most cases...the contrary can happen obviously as seen in hyenas, spiders or some types of fish.
You would need an enormous pressure.
In normal primates, it's better for a large primate to be male, because males have larger maximum numbers of offspring, and size helps it be dominant and impress the girls -- and it's better for a small primate to be female, because males also are more likely to have few or no offspring, being cut out by the larger males.
Every bit of food that goes to making a female larger is one that doesn't go to making another offspring. That females must invest much more in their offspring than males do means this is much more vital for them.
This is not a barrier as such, but it is an obstacle.
Perhaps you could have oases of plentiful food, but males must leave their childhood oasis for an adult one, and the long treks between them make large size unfeasible. Meanwhile, in the oases, a female's biggest pressure is other females, and so large size is necessary.
Edit: hmm -- then the male could travel while young and grow after. Perhaps the females would eject the males whenever there was a shortage, meaning a male always had to be ready to make the starvation-rations trek.
Edit 2: To eject the males, the females would have to be already larger or work in concert, but if they pull it off, those that eject males by size would be better off. Larger males are a larger burden on the food supply. Furthermore, if they are harder to fight, they are easier to corner; a smaller male could, say, climb a tree to boughs too small for the females to follow, and perhaps even forage for food there, thus further decreasing its impact on the practical food supply. Keeping around the smallest males would ensure there were some for when breeding became practical again at minimum cost.
The growth of a baby primate is generally quite effort intensive. For those non monogamous species of primates where the male doesn't put effort in paternal care, it could make sense that the female, being tasked with providing care to the infant(s), would develop a larger body in order to better suit the task, while the male, caring only about the mating, could be smaller.
On the other hand a larger body would mean also a larger energetic need: this cannot be satisfied by the male fetching more food in exchange for mating (else the bigger male would be favored), but maybe can be covered by sexual cannibalism, where the female eats the male after mating, like it happens with spiders and some insects: the female would offer her sexual favors to the male willing to mate with her, and once in a while one of those male would impregnate her.
The most extreme example of sexual dimorphism of the type you want occurs in a species of fish.
Some species of anglerfish [...] display extreme sexual dimorphism. Females are more typical in appearance to other fish, whereas the males are tiny rudimentary creatures with stunted digestive systems. A male must find a female and fuse with her: he then lives parasitically, becoming little more than a sperm-producing body. https://en.wikipedia.org/wiki/Sexual_dimorphism
Illustration by Dr Tony Ayling - File:Cryptopsaras couesii (triplewart seadevil).gif, CC BY-SA 1.0, https://commons.wikimedia.org/w/index.php?curid=5871051
As for primates, sexual dimorpjism does occur but usually in the opposite direction to what you want. The males are usually bigger than the females. The obvious example is that silver-back gorillas can only be male.
I suggest that you discover (or concoct) an evolutionary explanation for the dimorphism of the anglerfish and then have your world contain a similar environment that would cause primates to follow suit.
Of all the answers with arguments why there could be extreme sexual dimorphism, I'll add a prime reason why not: The size of the Y chromosome.
The Y chromosome is pretty much the smallest human chromosome, and other primates are little different. There is only so much that you can encode on a chromosome that small.
Now, that's not to say that with the right evolutionary pressures, that the extreme sexual dimorphism that the OP requires could not evolve, just that it would take a large number of changes on other chromosomes to make certain genes activate in the presence or absence of testosterone that would achieve the desired effect... and these changes would likely not be able to happen in a mere few million years. Ten to thirty million years, yes, but not under five or so.
A solid reason for such an extreme dimorphism could be an example like bone worms where due to lack of resources the majority of food goes to to child barring females and the males eat close to nothing basically existing just to make sperm and die. This is of course a very extreme example and likely wouldn't occur in mammals especially primates that tend to have low birth rates, Another reason could be territory defending or a need to birth a large litter (this would be in order to have enough live but to birth a ton this usually means lower quality babies, in other words less personal tending and all together less investment in their development) that would lead to a difference (need for larger child barring hips).If for territory, say the size of the primates as a whole was close to the males at first and there's a few good spots for raising children in the environment so competition between females for this resource would lead to them getting bigger and bigger as the larger they are the more likely they are to both scare off opposition and win if intimidation isn't enough. other reasons would be defending off predators of young ones, or a reverse role play of the stag beetle where low male count leads to competition between females.
