Chazal (Brachos 20) explain that Hashem shows favoritism towards Bnei Yisrael, "Yisa Hashem panav eilecha v'yasem lecha shalom," because we go the extra mile for Him -- even though birchas hamazon need only be recited if one is satiated, we recite it even after eating a k'zayis. Why is shalom in particular the reward for saying birchas mazon even on a k'zayis? And why are we rewarded davka for this particular case of going the extra mile and not some other case where we go above and beyond the d'orasya level in doing a mitzvah?
Chasam Sofer has a simple answer: One can only have peace when people are satisfied with what they have. If everyone always wants more than the k'zayis they have been doled out -- never happy until fully satiated -- there will always be jealousy and fighting. (On a related note, I saw a beautiful vort in the name of R' Dovid Povarski. The Nesi'im each brought the same items as gifts to the Mishkan, but each with a different intention. Just ask your teenage daughter if she would wear the same dress as a friend to an event -- lo yitachein! So how did each Nasi end up bringing exactly what the other ones brought? Because they paid absolutely no mind on what others were doing -- their eyes were only on their own world.)
The Ishbitzer goes a step further. Why can one be happy even with a k'zayis? Because it's not physical bread alone which satiates, but it is the "motza pi Hashem" found in the bread. If that pnimiyus is the ikar and the physical loaf is tafeil, then one can be happy with any amount. If you choose to look beyond the superficial and focus on the pnimiyus within, then Hashem will look beyond your superficial shortcoming and bless you with shalom (=shleimus) in turn.