What is the evolutionary purpose of envy? I am seeking for a general explanation within the context of evolutionary psychology. 

1) What is the purpose of envy?

2) Is it safe to assume that experiences with envy should reach a maximum during  peak reproductive years? Is it a causal relationship, or just correlation?

(To add to the above: At least in modern societies, where basic survival has been for the most part dealt with, how often can envy be ultimately traced back and attributed to primordial instincts?)

I also have a more specific question, which is the following:

3) In the context of a romantic relationship, assuming there are no other potential mates as external threats, and the two partners are not competing for resources in the same domain, are there any reasons for which romantic partners could be envious of each other?

I am not a psychologist, so please feel free to edit the question if you think it lacks specificity.
A lot of sources might be of use here, but one thing in your question is not clear to me - when you write "envy", do you mean a kind of resentment towards someone with material possessions that you don't have, or a jealousy in a romantic context? Everything that I would write is about the first meaning, and I have no idea about anything connected with the second. I don't really understand it, or questions number 2 and 3. Whence the data about it?

Basically, a negative feeling towards someone with a larger lot of things (like food) is quite easily understandable in an evolutionary context - someone with more goods has a larger chance to survive and produce an offspring, thus feeling bad about it motivates us to reduce the difference. As fitness is not absolute, but relative, reducing someone's fitness enlarges ours. More nuanced view would be that it rather motivates us and enhances cognitive abilities, and it is indeed what some have found - a link.

Somewhat different story comes from modern behavioral economics. It claims that humans have something that they call social preferences, or "other-regarding preferences" (Gintis 2009). An few examples - Fehr and Schmidt show that agents have a concern for the welfare of others and income distribution, with equality being preferred. Further studies has shown  that in experimental games, such as Ultimatum Game, Dictator’s Game or Prisoners’ Dilemma,  participants observing the interactions of others were punishing those who did not cooperate or share, although their interest was not involved and punishing itself was costly for them – they punished altruistically (Fehr and Gachter 2002). This also allowed for cooperation to flourish, while if such third-party punishment was not allowed, cooperation broke down. 

Fehr and Gachter’s data were then explained by postulating an evolutionary mechanism that brought about these patterns of behaviour - specifically group selection, which was deemed possible precisely because of altruistic punishment, in which individuals were acting in the interest of their groups at some cost for themselves. A bit different conclusions were reached by Charness and Rabin (2002), who claimed that participants were more concerned with increasing social welfare, especially that of the worst-off, rather than with equity, as was in previous models. Later, the Fehr and Gachter model of inequity aversion was challenged and the same data were said to better explained by egalitarian motives, which tend to lead to punishment of the highest earner (Fowler et.al. 2005).  

Thus, envy could be interpreted as really an urge to restore fairness. This urge might of course be a mistake, since some inequality could be fair, but for our hunter-gatherer minds it is still a bad thing. 

Some involve envy in their more general theories. For example, Binmore has a whole, somewhat complicated, game-theoretical explanation of fairness as an equilibrium-selection device. If you were to buy his theory, it would answer your first question - the purpose of envy in this theory is to maintain stable social system in hunter-gatherer bands, as large inequalities would lead to hierarchy and a possible dissolution of their social contract. Envy construed in such a way is also a criterion of fairness, not just for Binmore, but for quite many modern welfare economists: assignment of goods is deemed fair only if nobody envies the bundle of commodities assigned to someone else (while envying here means not only to compare just material goods, but also what comes with them - few would envy in this way a millionaire with a terminal cancer).