but a polearm would be too heavy and it would be too tiring to hold it all the time

That's just not the case. There's a common tendency to overestimate the weight of medieval weapons and armor. Swords, for instance, rarely weighed more than four and a half pounds, and were usually between two and three and one-half pounds. In general, polearm type weapons range from a low of about three pounds for a light spear, to a high of perhaps eight or nine pounds for a large halberd; poleaxes are in the middle, about six to seven and one-half pounds. These are not particularly heavy weapons, even when carried in the hands. Modern infantry carbines start at about eight pounds; machine guns weigh about 24-28 pounds; and mortars, even when disassembled for carrying, may have chunks that weigh more than thirty pounds. There's just no reason to think that a polearm would be an unmanageable burden.