Hi FallsHiker,
You're not alone in this area. Many new dancers, both men and women, are either not alerted to the importance of their frame (the teacher's fault), or they are not learning to dance with the purpose of obtaining some level of mastery of the finer aspect of couple dancing. Do some shoulder exercises to be prepared for the ladies who will "hang" on you. In a social dance setting, that is a reality you will face. There are ladies where I dance who make me pray for the song to end, and I am more fit than the average dancer. With the ladies I know well enough, I ask them to support their arms as they should. With some of the others, I grin and bear it as a gentlman should. I sometimes have to walk into the darkness to shake off the fatigue. I confess that I ask these ladies to dance on occasion just to be polite. Alas, it comes with the territory.