The problem with the weight in the original post (7lb 11 oz) was that it came from a weapon much longer than the in game weapon. I see that in the second version of the calculations you've revised it to 6.6 pounds, which I assume comes from the in game value of 2.8kg. Of course the in game value is unreliable as far as realistic weight goes, as it is adjusted both roughly on realistic values and game balance. This usually results in the weight on weapons in game being inflated slightly beyond their correct weights.
As far as correct weights go, the crow's beak and other similar pick type weapons were indeed quite heavy at the end. I think an accurate estimate of the weight would be perhaps 5 pounds, give or take a little bit. The myarmoury page you linked shows a fairly short version of a similar weapon as 105centimeters and 3 pounds 8 inches. It notes that it is possibly shortened, which if it is, it is the wood being removed from the base of the weapon, meaning that a full length version would still have a fairly close weight. The in game model of the bec is roughly 165 centimeters long, so I think 5 pounds should be a reasonable estimate.
Another note about balance: the bec is not a "balanced" weapon by any means in real life, but that does not necessarily translate to having poor handling characteristics. Poleaxes are actually quite wieldy weapons. In any case, considering that the length of the weapon is only in the 120s, it seems reasonable to have the weapon with the balanced tag to me.