The Gaussian spin-echo decay rate, 1/T-2G, of Cu-63, which is related
to the antiferromagnetic spin correlation length, xi, has been measure
d in overdoped TlSr2CaCu2O7-delta with T-c = 70 K, 52 K, and 10 K. It
has been found that the decrease of xi under a critical value makes th
e pairing interaction weaken, resulting in the marked suppression in T
-c with increasing holes.