  We introduce brane-worlds with non-constant tension, strenghtening the
analogy with fluid membranes, which exhibit a temperature-dependence according
to the empirical law established by E\"otv\"os. This new degree of freedom
allows for evolving gravitational and cosmological constants, the latter being
a natural candidate for dark energy. We establish the covariant dynamics on a
brane with variable tension in full generality, by considering asymmetrically
embedded branes and allowing for non-standard model fields in the 5-dimensional
space-time. Then we apply the formalism for a perfect fluid on a Friedmann
brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter
space-time.
