If you're interested in the history of language as well as the history of beer, you might want to take a look at this paper "Old English _Beor_" by Christine Fell (Leeds Studies in English, n.s. VIII, 1975, 76-95) (available online:
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In a nutshell, she concludes that while 'ale' probably meant ale back in olden times (when it was spelled 'ealu'), 'beor' almost certainly didn't mean beer. It appears to have been a sweet drink, stronger than wine, and based on honey. (Sweet because when it can't be had, suggested alternatives for it are sweetened wine and sweetened ale; strong because pregnant women are told to stay off it although they are only told to drink other drink in moderation; and based on honey because it is used as a gloss/translation of hydromel in Old English latin texts). Beor probably wasn't a grain-based drink at all. She concludes that the modern word beer is a loan word (from Dutch/German).
There's one piece of evidence that I couldn't really follow. A pint of beor was supposed to weight 22 pennies less than a pint of water (whereas a pint of ale supposedly weighed six pennies more and a pint of wine 15 pennies more (if I recall correctly)). This supports saying beor was strong, because its final gravity must have been less than 1.000, but how is that consistent with its being sweet? and why is ale lighter than wine?