The chains are peculiar yes, but not that peculiar: It's strongly ingrained in us to return favours, to the point that giving someone something is a brutally effective way of exploiting them by later asking for a bigger favour back (e.g. consider Hare Krishna, that tended to use flowers for this purpose). The effect is so strong that we often try to prevent receiving favours because we don't want to become indebted.
In that light, these chains are easy to explain: People might like the idea, but people are also likely to want to prevent a feeling of being indebted - if you can't pay back the person who did you the favour, paying it forward to the person is the next best thing. There's also social pressure to show that you're as charitable as the guy in front of you, and against being seen as the person who is either "too greedy" or too poor.
There's also very low perceived cost: You were intending to pay for your meal anyway; that you're actually paying for someone elses meal makes little difference for you - it's more like friends that takes turn paying the bill when going out, where it is a social gesture rather than an attempt at charity.
The idea is that if I ask a favor of you (to loan me a book, in Ben's case) - you are more likely to become friendly to me in the future.
Its a curious extension of what you mentioned above, by asking you for a favor - which you then grant - you gain a sort of psychological 'credit' over me (I owe you). In fact, because you implicitly recognize that I'm voluntarily offering to place myself in your debt, you are happy to oblige since you recognize the subtle power relationship at work.
I learned about this from a lawyer friend who claims he uses it all the time. If there is someone professionally he want to get to know, he will call them and ask them for a small favor (ie. I can't make the social gala party tonight, could you please take my check with you and drop it off to pay for my yearly dues...etc).
I use this occasionally for social, not professional, purposes and it seems to work quite well.
It’s sometimes a bit tricky to think up a favor the right size for the state of your relationship, but still useful enough to be real. Fake favors don’t work (and are frankly just weird).
You were intending to pay for your meal anyway; that you're actually paying for someone elses meal makes little difference for you
These chains have been common at coffee shops drive-thrus in Canada for years, where the standard deviation of orders is very small: Almost everyone is just getting a coffee and maybe a donut. A couple of dollars, generally. I have to imagine that order size varies much more dramatically at a burger shack, and it has to suck if you and getting your cheeseburger and end up in a chain with a family of six behind you.
In that light, these chains are easy to explain: People might like the idea, but people are also likely to want to prevent a feeling of being indebted - if you can't pay back the person who did you the favour, paying it forward to the person is the next best thing. There's also social pressure to show that you're as charitable as the guy in front of you, and against being seen as the person who is either "too greedy" or too poor.
There's also very low perceived cost: You were intending to pay for your meal anyway; that you're actually paying for someone elses meal makes little difference for you - it's more like friends that takes turn paying the bill when going out, where it is a social gesture rather than an attempt at charity.