I am an ex-powerlifter and currently bodybuilding. I do sometimes have a hard time showing my students that very little if no strength is used in aikido. Usually to get the point across (especially to my bigger students) I have to let them feel my technique and energy individually. I am lucky though, I have 3 students that are between 320lbs and 350lbs so it makes my 250lb frame look small.
As for cutting loose; Once a week I train with other dan ranks for a couple of hours and usually we wind up doing some jiyu-waza. I find this less fun though, because being a cautious nage, I am constantly worried about causing any injury to my friends. I can't say that I am comfortable with "cutting loose" because I've only been studying aikido for 12 years and I don't believe I have the control necessary to go full out without causing injury. (Maybe in another 20 or 30 years)