Weight IS a factor for Morris players. I have a light Morse and a heavy Jeffries; the difference is huge in terms of pressure on the tendons of the hands and arms, muscular tiredness, etc.

As you point out, a neck strap/cord can help, but i've tried it and find it constricting. Also, many of us are wary about marring expensive vintage instruments with strap fasteners.

The answer, in my humble opinion, is physical conditioning: exercises to strengthen the arms, smart stretching, etc. Then weight is much less of a factor.

Weight is less of a factor for those who can play seated.