Zweihander is wielded by two hands not because of its weight (lifting and hurling around 5kg, hell, even 10kg can be completely trival for even beginner body builders). Zweihander is wielded by two hands for superior control and power. Because of its large size, it would be very easy to lose balance wielding it with a single hand.
There are many misconceptions about two handed swords. First, they were light… Very light. My previous cat weighed more than most zweihanders. Granted he was a fat bastard, but still.
Most people that can do a pull up should easily be able to manouver 5 to 10 kg sword with both hands.
And take note, most two handers actually weight less than 5kg. Rather they usually weigh about 3.5kg. What made them harder to maneuver was really the fact that they were pretty long, which is why a great number of them used compound hilts, to make parrying more effective at short ranges.
Secondly, they were infrequent, and later mostly substituted by longswords or hand-and-a-half swords as far as i know. The reason for this was that two handed sword were created when some warriors desired a blade that you could use two hands with, to deliver more power into their blows.
Zweihanders adopted a design which allowed warrior to more or less balance speed and striking power by keeping the weight relatively low, and making them longer with a longer hilt for more maneuverability. Still, they were very clumsy to wield.
The bastard sword was however, also pretty good at penetrating armor, and because of added maneuverability and speed and the ability to be used with a shield, it ended up being the most widely used weapon.
The two handed sword was in it’s essence a specialty weapon, mixing reach and power with more maneuverability than a lance or a pike, and employed mostly in distinct situations rather than all over the battlefield afaik.