Hmm. I have amps with current rating, eg., 45 amps, 40 amps, 60 amps. One of them is not difficult at all to lift. Very light in fact, an old Mission Cyrus One integrated that feels like it weighs a pound or two. Yet it was rated at 40 amps, but only 25 wpc. Now, I'm sure you think that's just marketing talk, but the fact is that I used to drive a pair of KLH 5's with it(about 77db efficiency) and it's never had trouble with any pair of speakers. It is a little light on the very bottom, a little warm in the upper bass and seriously rolled off in the treble, but still a very musicallly dynamic little amp.
In general, however, the heavier amps do seem to be rated for higher current.
In general, however, the heavier amps do seem to be rated for higher current.