We present results from daily monitoring of gamma rays in the energy range $sim0.5$ to $sim100$ TeV with the first 17 months of data from the High Altitude Water Cherenkov (HAWC) Observatory. Its wide field of view of 2 steradians and duty cycle of $>95$% are unique features compared to other TeV observatories that allow us to observe every source that transits over HAWC for up to $sim6$ hours each sidereal day. This regular sampling yields unprecedented light curves from unbiased measurements that are independent of seasons or weather conditions. For the Crab Nebula as a reference source we find no variability in the TeV band. Our main focus is the study of the TeV blazars Markarian (Mrk) 421 and Mrk 501. A spectral fit for Mrk 421 yields a power law index $Gamma=2.21 pm0.14_{mathrm{stat}}pm0.20_{mathrm{sys}}$ and an exponential cut-off $E_0=5.4 pm 1.1_{mathrm{stat}}pm 1.0_{mathrm{sys}}$ TeV. For Mrk 501, we find an index $Gamma=1.60pm 0.30_{mathrm{stat}} pm 0.20_{mathrm{sys}}$ and exponential cut-off $E_0=5.7pm 1.6_{mathrm{stat}} pm 1.0_{mathrm{sys}}$ TeV. The light curves for both sources show clear variability and a Bayesian analysis is applied to identify changes between flux states. The highest per-transit fluxes observed from Mrk 421 exceed the Crab Nebula flux by a factor of approximately five. For Mrk 501, several transits show fluxes in excess of three times the Crab Nebula flux. In a comparison to lower energy gamma-ray and X-ray monitoring data with comparable sampling we cannot identify clear counterparts for the most significant flaring features observed by HAWC.
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