  Sen attached to each p-adic Galois representation of a p-adic field a
multiset of numbers called generalized Hodge-Tate weights. In this paper, we
discuss a rigidity of these numbers in a geometric family. More precisely, we
consider a p-adic local system on a rigid analytic variety over a p-adic field
and show that the multiset of generalized Hodge-Tate weights of the local
system is constant. The proof uses the p-adic Riemann-Hilbert correspondence by
Liu and Zhu, a Sen-Fontaine decompletion theory in the relative setting, and
the theory of formal connections. We also discuss basic properties of
Hodge-Tate sheaves on a rigid analytic variety.
