Sexual dimorphism the difference between average male and female body size is the primary determinate of "polygynousness"...
The classic reason for one sex to be larger than the other is competition within the LARGER sex for mating with the smaller.
Basically, in mammals this means big MALES, with lots of low-cost sperm, competing for the opportunity to fertilize the female's precious eggs the female, having invested much more in each egg, can afford to be really fussy about who gets to fertilize it...
If she chooses (directly, as in the classic 'female choice', or indirectly, as with joining a harem) bigger males then males will get BIGGER! If she chooses colorful males, then males get gaudy. If she chooses males which hang around and help bring up the young, then males get faithful and helpful. If she chooses males with shiny silver sports cars...well you get the idea.These are the general patterns. In those circumstances where parental care is necessary to ensure the survival of the offspring, a male can be pulled (kicking and screaming) into looking after its brats and easily get left holding the baby so to speak.
In fish and amphibians with external fertilization and where the female has lots and lots of low-cost eggs, the very nature of the act means the male is often the LAST to have contact with the eggs giving the female the opportunity to scoot off and leave him with the job of parental care. (There are many excellent examples of good daddy fish, such as sea horses.) Where fertilization is internal such as amniotes, the female can't do it this way, but males can be made to be better parents than females if the species goes through a situation where the care of both partners is essential to successful reproduction.
If conditions then become less harsh, each will have an equal chance in evolutionary time, to take off first leaving the other with sole responsibility for care of the young. Sometimes it will be the male, other times the female there are a number of examples in bird species where the males look after the young (phalaropes are one). With mammals (remember mammals; this page is about MAMMALS) this behavior is rare, but I can assure you not IMPOSSIBLE. In almost all mammals there is a huge initial imbalance in investment: not only do females produce the egg, but they gestate and suckle (ignoring the arrival of babe formula) the young.
In situations where the male is the sole carer, it is now he, rather than the female, who has the most to offer a prospective romantic interlude. And it will thus be she who must compete for his compliance. Leading, perhaps, to selection for larger females
There's evidence for this in recent research on the Raptors - the original ones, not the Toronto basketball team. And of course the female, freed from the burden of maternal responsibilities, can now indulge in polyandry - ie: mating with a number of males, leaving each mate to look after the resulting offspring. (Phalaropes are good examples - the female manages up to three broods, each with different mates, in the short Arctic summer.) With polyandry the selective pressures for larger females are even stronger - recent evidence indicates "T-REX" was in fact a bit of a runt - standing next to his even larger and powerful mate: the "T-REXette"!
Things sure might be different around here
- if not for that astroid!