they say it's feather-weight. i'm sure it is- it's flash based and uber-small whether or not it looks stupid around your neck is another story...
It's 1.5 ounces, the Shuffle is around .8 I think. Steve Jobs said it weighs less than 8 quarters. I think the nano will hang comfortably from a lanyard, it's much closer to the Shuffle in weight than the Mini. The nano doesn't come with a lanyard, but 3rd party ones should be available soon. Or you can just rig one up yourself.
It's light, but you wouldn't want to wear it around your neck if you were going to be running... if it pops up and hits you in the nose (or, in my case, my glasses), you'd definitely feel it.
DIY strap. How about DIY strap. It's easy and cheep way. http://tokiolapalm.cool.ne.jp/giken/index.html