Well, my views on the weight of bows are already posted elsewhere on the site and like Steve, I have a veeeery hard time imagining an army averaging 120#. Individuals - fine, but as soon as you try to extrapolate that to the majority of your troops, the median would drop.
I'll put in my tuppeny worth just for laughs. From the point of view of the strength of the idividuals, the hey day of the archer would have been up to the mid 1340's. The reason for this is that at that point in time, the population in Britain exceeded the capacity to provide sufficient food with available technology and the size of the parcels of land occupied by those people. Essentially, a significant proportion of the population were involved in agriculture and most of them had to supplement the table with hunted food - hence the fact that the bow in England was regarded as a 'way of life' by continentals. The method of breaking earth with a plough of that time involves a push pull movement together with anchor on a wide stance and rotation of the hips - very similar to drawing a big bow. The strength came from day to day activities, therefore, not practice with the bow.
After the mid 1340's, the great plagues had killed off enormous swathes of the population and those left alive found themselves better off and occupying bigger parcels of land. They needed to hunt with the bow less often and decline in the use of the bow commences at this stage as a result. The laws requiring Sunday archery practice post date the plagues for this reason (first one by Edwd 2nd in 1365 I believe but I'd have to check).
By 1415, guns had to started to appear although the bow was still the major artillery weapon. It was becoming hard at this time to raise and maintain large archer armies.
Jumping forwards towards the tudor period - many archers were no longer engaged in agrarian activity, hence the bewailing of loss of strength in our manhood etc etc. Its worth noting that by Tudor times there was an awareness that an archer, in order to shoot strong shots, needs his three meals a day and to sleep warm in a bed at night - hence the growing popularity of firearms at that time.
So you see, its not about bows - its about the people. I think its likely that the requirements of the bows by the tudor times would have been greater than those of the 1340's - armour became better and more available after all. As a result, I'd guess you had a problem of needing to make the bows heavier at a time when the people were weakening for the reasons outlined above. Either way - it still makes me think that the longbows averaged in the 100-110# range and not more. After all, we aren't talking about anything sophisticated here - it is just a stick made of a softwood. I'm prepared to accept that the quality of wood might have been better in the past - but in percentage terms it wouldn't have been THAT much better than the best yew wood today. Equally, the medieval bowyers knew what they were doing - but again, in percentage terms, they won't have been THAT much better than a Roy King or a Pip Bickerstaffe.
Anyway, thats my take on things.
ChrisD