Was it common for farmers and those not in the noble classes to have weapons for self defense? maybe a farmer having a bow and arrow to defend against wolves? And were some weapons exclusively for the nobility?
In Iceland it certainly, from a Saga perspective (from the viewpoint that they reflect society in the Sturlung period, that is from about 1200 onwards) does not seem uncommon for 'farmers' (in Medieval Iceland nearly everybody was a farmer, as there were not urbanised areas/ towns|), or lower class landowners, to possess an axe or spear at least.
Axes and spears have the virtue of being relatively cheap to make; only a small amount of poor quality iron was necessary, and although I am not convinced by the argument axes did have utilitarian purposes.
Have a look at this thread, which is not quite the same question, but has some relevant information.