Atemi does not need weight in all circumstances.
...Touch the eyelid of your Uke. Don't warn them!.... That's Atemi!
Strike the ribs! ...That's Atemi!
Strike full power to the side of the neck.... That's Atemi.
...Shock is what you need to induce!
I really enjoyed reading everyone's responses in this thread so far, but I would like to add my two cents worth.
To begin with, the term atemi may be referred by some as striking vital organs or causing a distraction in the opponent. I think this is a less than complete view of the term, as there are other terms to describe the above two situations, such as kyushojutsu or creating suki. The word atemi means something akin to "fortuitous happening" and one of my Japanese dictionaries calls it a "knockdown blow". I like to think of it as a "scoring blow", one that would take the opponent out of the fight more than just momentarily (if they respond to the creation of atemi through ukemi, then it might be a "distraction" between a striking technique and a throwing technique) and my first intent would have been the striking technique designed to put the opponent out of the fight with a single blow.
Perhaps another way to look at it, since most aikidoists claim that their art is the unarmed version of swordsmanship, is through the eyes of an armed engagement. Cutting a man down with any sort of wielded weapon requires stability, structure, target, awareness of distance and timing. Translating this into unarmed fighting is how I equate atemi. If you could cut someone down for real, you have the opportunity to delivery real atemi (either softly and overwhelmingly or smashing or punishing or....).
Have to get back to work....