  (Abridged) We present a systematic study of weak intervening CaII absorbers
at low redshift (z<0.5), based on the analysis of archival high resolution
(R>45,000) optical spectra of 304 quasars and active galactic nuclei observed
with VLT/UVES. Along a total redshift path of Dz~100 we detected 23 intervening
CaII absorbers in both the CaII H & K lines, with rest frame equivalent widths
W_r,3934=15-799 mA and column densities log N(CaII)=11.25-13.04. We obtain a
bias corrected number density of weak intervening CaII absorbers of
dN/dz=0.117+-0.044 at z=0.35 for absorbers with log N(CaII)>11.65. This is ~2.6
times the value obtained for damped Lyman alpha absorbers (DLAs) at low
redshift. From ionization modeling we conclude that intervening CaII absorption
with log N(CaII)>11.5 arises in optically thick neutral gas in DLAs, sub-DLAs
and Lyman limit systems (LLS) at HI column densities of log N(HI)>17.4. The
relatively large cross section of these absorbers together with the frequent
detection of CaII absorption in high velocity clouds (HVCs) in the halo of the
Milky Way suggests that a considerable fraction of the intervening CaII systems
trace dusty neutral gas structures in the halos and circumgalactic environment
of galaxies (i.e., they are HVC analogs). Considering all galaxies with
luminosities L>0.05L* we calculate that the characteristic radial extent of
(partly) neutral gas clouds with log N(HI)>17.4 around low-redshift galaxies is
R_HVC ~ 55 kpc.
