We present a large high-resolution study of the distribution and evolution of C^IV^ absorbers, including the weakest population with equivalent widths W_r_<0.3{AA} . By searching 369 high-resolution, high signal-to-noise ratio spectra of quasars at 1.1<=z_em_<=5.3 from Keck/HIRES and VLT/UVES, we find 1268 C^IV^ absorbers with W_r_>~0.05{AA} (our ~50% completeness limit) at redshifts 1.0<=z<=4.75. A Schechter function describes the observed equivalent width distribution with a transition from power-law to exponential decline at W_r_>~0.5{AA} . The power-law slope {alpha} rises by ~7%, and the transition equivalent width W* falls by ~20% from <z>=1.7 to 3.6. We find that the comoving redshift path density, dN/dX, of W_r_>=0.05{AA} absorbers rises by ~1.8 times from z~4.0 to 1.3, while the W_r_>=0.6{AA} dN/dX rises by a factor of ~8.5. We quantify the observed evolution by a model in which dN/dX decreases linearly with increasing redshift. The model suggests that populations with larger W_r_ thresholds evolve faster with redshift and appear later in the universe. The cosmological Technicolor Dawn simulations at z=3-5 overproduce the observed abundance of absorbers with W_r_<=0.3{AA} while yielding better agreement at higher W_r_. Our empirical linear model successfully describes C^IV^ evolution in the simulations and the observed evolution of W_r_>=0.6{AA} C^IV^ for the past ~12Gyr. Combining our measurements with the literature gives us a picture of C^IV^ absorbing structures becoming more numerous and/or larger in physical size over the last ~13Gyr of cosmic time (z~6-0).