A 2011 paper by Thomas Klein, called "Durch Dick und Dünn: Zum Einfluss von Partnerschaft und Partnermarkt auf das Körpergewicht", studies the intersection of mating and health-related outcomes, namely the BMI. Here's the English-language abstract to the paper which is both written in German and gated for maximum inaccessibility:
This article analyzes how body weight is associated with the existence of an intimate partner and with the sex ratio in the marriage market. The data rely on a representative sample of the 16–55 years old population in Germany, carried out in 2009 (Partner Market Survey 2009). In this data set, individuals’ mating opportunities for the first time are measured by their integration in a network of friends as well as in foci of activity as conceptualized by Scott Feld. Results confirm a weight increase after an intimate relationship has started (negative protection) and they also confirm a mating disadvantage corresponding to high weight (selection). Further results lead to the discovery that the weight difference between individuals with and without a partner varies according to the sex ratio in the marriage market: higher competition in the marriage market obviously corresponds to relatively lower weight of individuals without partner. Moreover, similar BMI of partners is not a result of adaption between partners over time but solely is a result of assortative mating. Consequently, mating patterns with respect to obesity have no effect on the individuals’ weight.
So, there is a number of results; I'll highlight two. Perhaps the most convincing one gives an answer to a question many people will have wondered about (and that, according to the author, no previous study has addressed): How come partners are similar in BMI? According to Klein's results, this is solely a selection effect; treatment - measured as the coefficient yielded by an interaction between the partner's BMI and the length of the relationship - seems to play practically no role.
Another key finding is that single people (but not others) appear to react to the sex ratio in their social circles: When there are more potential partners and fewer competitiors, they exhibit higher BMIs (controlling for other stuff). It's as though people don't try as hard when there's little competition. I have a few quibbles with these analyses, however. It's unclear exactly how the sex ratio measure was operationalized and it is never explained why it was logged rather than used in its original (linear) form, which would seem the most plausible functional form a priori. Further, Klein asserts, but does not show, that only the sex ratio in a person's social circles counts - I would have liked to see the local sex ratio as an additional independent variable. I also bet the size of the local market has an influence. More generally, none of the regressions presents a particular identification strategy beyond controlling for confounds.
Nonetheless, these are interesting results. There are (at least!) two views on when rational choice explanations will not work so well. One holds that rational choice will work poorly when decisions involve strong emotions. Another is that rational choice cannot contribute much to explaining decisions when the stakes are low, but will be powerful when they are high. The continuing flow of results showing that rational choice has a lot to contribute to the study of mating is evidence in against the former view, and in favour of the latter.