Other questions have covered what the physical structure of a humanoid giant might look like. Assuming that anatomically modern humans (or something close) were dispersed into several distinct population groups over an adequate time span, what evolutionary path might cause one of these groups to become giants?
Giants in this case meaning a mostly human-ish creature about 10 feet tall, perhaps with a general build resembling gigantopithecus. One big problem is, from what I understand, size in mammals is usually driven up by competition between males over females. But in this case I'd like the female giants to be noticeably (i.e. several feet) taller then the males, and form the dominant and more sedentary core of their communities. I'd like to do this is the simplest and most plausible way available, keeping them otherwise as close to the human baseline as I realistically can.
Ideally, these giants might evolve on a rainy tropical archipelago, in which the largest landmass is a bit less than half the size of Australia. This would be convenient for me, however it is not required. I can pretty easily tweak the world or their origin point to fit a good evolutionary path.
EDIT: Just to clarify for posters, "matriarchal" is title question shorthand for "sexually dimorphic with larger females", which I tried to specify in the text below. I certainly appreciate the deep importance of culture, but this question is about justifying a physiological difference, not about ways to produce a matriarchal culture for giants. I plan for the size difference to have a wide variety of social effects, beyond just power structures. Thanks!