  Weights of edges and nodes on food webs which are available from the
empirical data hide much information about energy flows and biomass
distributions in ecosystem. We define a set of variables related to weights for
each species $i$, including the throughflow $T_i$, the total biomass $X_i$, and
the dissipated flow $D_i$ (output to the environment) to uncover the following
common patterns in 19 empirical weighted food webs: (1) DGBD distributions
(Discrete version of a Generalized Beta Distribution), a kind of deformed
Zipf's law, of energy flow and storage biomass; (2) The allometric scaling law
$T_i\propto X_i^{\alpha}$, which can be viewed as the counterpart of the
Kleiber's 3/4 law at the population level; (3) The dissipation law $D_i\propto
T_i^{\beta}$; and (4) The gravity law, including univariate version
$f_{ij}\propto (T_iT_j)^{\gamma}$ and bivariate approvement $f_{ij}\propto
T_i^{\gamma_1}T_j^{\gamma_2}$. These patterns are very common and significant
in all collected webs, as a result, some remarkable regularities are hidden in
weights.
