  One of the central goals of the Spitzer Legacy Project ``From Molecular Cores
to Planet-forming Disks'' (c2d) is to determine the frequency of remnant
circumstellar disks around weak-line T Tauri stars (wTTs) and to study the
properties and evolutionary status of these disks. Here we present a census of
disks for a sample of over 230 spectroscopically identified wTTs located in the
c2d IRAC (3.6, 4.5, 4.8, and 8.0 um) and MIPS (24 um) maps of the Ophiuchus,
Lupus, and Perseus Molecular Clouds. We find that ~20% of the wTTs in a
magnitude limited subsample have noticeable IR-excesses at IRAC wavelengths
indicating the presence of a circumstellar disk. The disk frequencies we find
in these 3 regions are ~3-6 times larger than that recently found for a sample
of 83 relatively isolated wTTs located, for the most part, outside the highest
extinction regions covered by the c2d IRAC and MIPS maps. The disk fractions we
find are more consistent with those obtained in recent Spitzer studies of wTTs
in young clusters such as IC 348 and Tr 37. From their location in the H-R
diagram, we find that, in our sample, the wTTs with excesses are among the
younger part of the age distribution. Still, up to ~50% of the apparently
youngest stars in the sample show no evidence of IR excess, suggesting that the
circumstellar disks of a sizable fraction of pre-main-sequence stars dissipate
in a timescale of ~1 Myr. We also find that none of the stars in our sample
apparently older than ~10 Myrs have detectable circumstellar disks at
wavelengths < 24 um. Also, we find that the wTTs disks in our sample exhibit a
wide range of properties (SED morphology, inner radius, L_DISK/L*, etc) which
bridge the gaps observed between the cTTs and the debris disk regimes.
