Why do the two sexes have different reproductive costs and capabilities?
I may have misunderstood your question, but there is no theory why usually reproductive costs are on the female, as this is a fact. Females have usually larger (and fewer) reproductive cells (gametes), they frequently have to carry the embryo until birth, and sometimes they have to attend to the offspring during the first stages of their lives. To put it very simple, females are stuck with their offspring from the moment of conception until they are born - sometimes even longer - while males generally can mate with many females in a short period of time, potentially having much more offspring.
A consequence of this is that, usually, females are choosy (they want good mates), whereas males just try to mate as much as possible. Female choosiness generates sexual competition, as females prefer to mate with males having certain characteristics that hint to a superior genotypes/phenotype that may be passed to their prole (e.g. beautiful plumage, social status, size of the wallet). Sometimes the costs of attending offspring after birth are higher than the costs associated with reproduction alone. In some of these cases, we may observe unusual behaviors, e.g. male-only parental care and choosy males.
This is a very broad and complex topic and a short answer here cannot cover all of it. John Maynard Smith developed the game theory approach most commonly used to investigate the consequences of different pay-offs for the two sexes and to explore how these can influence the behavior of the parents. Moreover, this topic is also covered in many behavioral biology textbooks. I have had very positive experiences with Krebs &amp; Davis Behavioural Ecology (ISBN-13: 978-0865427310), which I would recommend.
Hope to have clarified some of your doubts.
Cheers,
Emilio