I apologize if this is an overly broad question. As far as I know, and I may be wrong, the middle ages, and subsequent eras, especially during the industrial revolution could be described as having population shifts, people leaving their small towns to go to cities. My question is about the populations of these small rural towns.
Is there a typical small farm town in Europe, over the course of 500 years or so would its population remain relatively stable? If so how did this happen? Did the replacement rate roughly match the death rate or were people leaving the towns. Or were these small towns just growing, by and large? If there was a time when the population suddenly started increasing was this do to changes in technology, or a decision to start making larger families for economic reasons?
Population studies is not my flair area, but one that I have read about a bit. One of my favorite websites is the GGDC.net which hosts a lot of population studies data, and papers explaining their methodologies.
As far as population growth, well, there were many many many factors. Since you seem to be struggling to form a good question, maybe you are interested in reading about the heavy plow and its impact on the population of "northern" Europe.
There are also many other factors that can be considered, such as the black death's uneven spread and climate variations. Which you can go into more detail in the references below.
References:
Big question: how do we get data. Because numerical datas aren't very easy to come by and their reliability on their own and as for other geographical or time spans is not always solid. So you have to use other sources, like literary sources, but forget about numerical precision. That's not completely a medieval thing and more often than not a modern thing for quite a lot of places/people (not just for Europe: just think about demography/genealogy of black slaves in Northern America, to quote something I've familiar with despite my education).
In short... It would much depend on the moment (is the 500 year span a time of growth or are you considering stagnation or crisis), the geographical area (migrations, populating policies by various political entities, decision to grand privileges or privileged status and so on) and the other economical activities- like cloth making, animal husbandry, or commerce- that went on (the typical farmer's family would get involved in more than one activity, and that's involved with technology as much as economy- preference for a certain type of an item- as well as political structure, i.e. locally self-governed communities could do a nice job of expanding population). Also, the size of family could be easily influenced by customs such as agrarian contracts (the introduction of sharecropping comes to mind) that are very local in their trends, and no always similar in re chronology of implementation.
1000 years are too much for a simpler or more detailed answer. There are roughly a population increase ca VIII century onwards, stagnation from late XIII century and crisis in the XIV (but you do get quick rebounds after catastrophies such as 1348 or 1361 plagues, even if population is not reaching the early XIII century-optimum). I'd say small towns follow these lines, but again, you have to consider it more locally.