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We introduce the Abnormally Weighting Energy (AWE) hypothesis in which darkenergy (DE) is presented as a consequence of the violation of the weakequivalence principle (WEP) at cosmological scales by some dark sector. Indeed,this implies a violation of the strong equivalence principle (SEP) for ordinarymatter and consequent cosmic acceleration in the observable frame as well asvariation of the gravitational constant. The consequent DE mechanism build uponthe AWE hypothesis (i) does not require a violation of the strong energycondition $p<-\rho c^2/3$, (ii) assumes rather non-negligible direct couplingsto the gravitational scalar field (iii) offers a natural convergence mechanismtoward general relativity (iv) accounts fairly for supernovae data from variouscouplings and equations of state of the dark sector as well as densityparameters very close to the ones of the concordance model $\Lambda CDM$.Finally (v), this AWE mechanism typically ends up with an Einstein-de Sitterexpansion regime once the attractor is reached.Comment: 3 pages, 1 figure, prepared for the Proceedings of the 11th Marcel  Grossmann Conference, held in Berlin, Germany, July 200

AN AWESOME HYPOTHESIS FOR DARK ENERGY: THE ABNORMALLY WEIGHTING ENERGY