A couple thoughts:
1. There are certain practical limitations to the weight a wooden bow can pull and still maintain portability, performance, etc. With the high quality Yew that was available to the English in Medieval times, the upper-limit based on materials would have been in the neighborhood of 120-200#s. So, strictly from a stave standpoint, there was no reason why they would have to avoid heavy bows.
2. There are certain human factors involved as well. Fit male archers would not be able to pull 1,000 pound bows but with the English style of draw they could probably all pull well over 100#s with the training they received. My pastor has a background in manual labor and he picked up one of my 100+ pound warbows and just pulled it without a problem--I just had to show him how. Within the English 'shooting in the bow' style, I'd bet that a 9-year-old boy could pull a 45# bow so why hand it to a trained military professional to shoot at armored men?
3. Heavy bows have two obvious advantages--penetration and distance. There is no war context in which penetration and distance are not desirable attributes for a bow to have.
Honestly, I probably get a little too 'romantic' about the weights of old warbows but I don't see any reason for a military to build bows far under the potential of their staves, or for fit, grown men to shoot light bows at armored soldiers.
I would suspect that most of the bows were over 100#s with few exceptions. But then, everyone knows what I think. Ha, ha.
J. D. Duff