  A typical formula of multiple zeta values is the sum formula which expresses
a Riemann zeta value as a sum of all multiple zeta values of fixed weight and
depth. Recently weighted sum formulas, which are weighted analogues of the sum
formula, have been studied by many people. In this paper, we give two formulas
of weighted sums with two parameters of multiple zeta values. As applications
of the formulas, we find some linear combinations of multiple zeta values which
can be expressed as polynomials of usual zeta values with coeffcients in the
rational polynomial ring generated by the two parameters, and obtain some
identities for weighted sums of multiple zeta values of small depths.
