  We study the distribution, in the space of Satake parameters, of local
components of Siegel cusp forms of genus 2 and growing weight, subject to a
specific weighting which allows us to apply results concerning Bessel models
and a variant of Petersson's formula. We obtain for this family a quantitative
local equidistribution result, and derive a number of consequences. In
particular, we show that the computation of the density of low-lying zeros of
the spinor L-functions (for restricted test functions) gives global evidence
for a well-known conjecture of B\"ocherer concerning the arithmetic nature of
Fourier coefficients of Siegel cusp forms.
