It is a bit too soon to see what post-publication peer-review will say about this, but noted Skeptic and evolutionary biologist, Professor P.Z. Myers has posted at his Pharyngula blog:
the paper doesn’t show a causal relationship.
Actually, they do do what they say: they present a mathematical model of how a disparity between head size and pelvic canal size could hypothetically lead to a selection effect, given a particular frequency of disproportion. They don’t actually measure or observe anything, though. They pull together a number of factors, like the heritability of pelvic and head size, and estimates of the frequency of serious birthing difficulties, etc., all of which show a wide range of reported values, and then put together an abstract series of calculations to show that hey, this could potentially have an effect. That’s it. Don’t panic. We’re not looking at an imminent future of bulbous-headed babies and pencil-hipped women because we’ve removed an important constraint on selection.
I concur with his assessment that this study is not an experiment that actually measured the heads of babies born over decades, found that it was increasing, and said that was because of caesareans. Instead, it is a theoretical mathematical model that predicts that there should be an increase:
We predict that this weak directional selection has led to a 10 to 20% increase in the rate of fetopelvic disproportion since the regular use of Caesarean sections.
Unrelated to the paper, there have been some comments on the loose use of terminology in the BBC article and in the question. "Affecting evolution" is a vague term. Natural selection can have a measurable effect on population distribution within one generation.
I got hung up on your phrase "This is only a couple of generations, which I do not think is enough for evolutionary effects to present themselves." You seem to think that an evolutionary effect involves a change in biology, which I don't think is the case.
Disclaimer: I have not read the full paper, but I do want to make the following point:
A single generation can be well enough for an evolutionary effect to present itself.
By means of a very simple example, assume there are no men. Every woman will be pregnant exactly once (holy spirit!); due to some gene, 1% of all babies are too large to deliver safely; the babies are all girls; they all inherit the gene of having too large babies; half of them die at birth. Consider this an equilibrium state. Now you introduce CS at time x, saving all babies. Only a single generation later, the rate of too large babies will be approximately 2% (in fact, 200/101) -- close to 100% more!
As a kind of explanation, note that an evolutionary effect does not necessarily mean that babies grow differently; it may simply be possible that the selection of babies of different sizes changes over time. In fact, the paper suggests exactly that:
We demonstrated that due to these three properties weak
directional selection favoring large neonates relative to the
maternal pelvic dimensions is sufficient to account for the high
incidence of fetopelvic disproportion in human populations.
Which, in my opinion, says exactly what I started with: there is not necessarily a change in biology; the observed size change can be explained without assuming any change in biology.
Finally, I feel the wording of your question title reflects that misunderstanding: CS are not affecting evolution (your question title); the selection through CS has an "evolutionary effect" (BBC article) in the sense that it is evolution.