  We show that if X is any proper complex variety, there is a weight
decomposition on the real schematic homotopy type, in the form of an algebraic
G_m-action. This extends to a real Hodge structure, in the form of a discrete
C^*-action, such that C^* x X -> X^{sch} is real analytic. If the fundamental
group is algebraically good, and the higher homotopy groups have finite rank,
this gives bigraded decompositions on the complexified homotopy groups. For
smooth proper varieties, the Hodge structure can be recovered from the
cohomology ring with coefficients in the universal semisimple local system.
