We present rest-frame Ly alpha equivalent widths (EW0) of 417 Ly alpha emitters (LAEs) detected with Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT) at 2.9 < z < 6.6 in the Hubble Ultra Deep Field. Based on the deep MUSE spectroscopy and ancillary Hubble Space Telescope (HST) photometry data, we carefully measured EW0 values taking into account extended Ly alpha emission and UV continuum slopes (beta). Our LAEs reach unprecedented depths, both in Ly alpha luminosities and UV absolute magnitudes, from log (L-Ly alpha/erg s(-1)) similar to 41.0 to 43.0 and from M-UV similar to -16 to -21 (0.01-1.0 L-z=3(*)). The EW0 values span the range of similar to 5 to 240 angstrom or larger, and their distribution can be well fitted by an exponential law N = N-0 exp(-EW0/w(0)). Owing to the high dynamic range in M-UV, we find that the scale factor, w(0), depends on M-UV in the sense that including fainter M-UV objects increases w(0), i.e., the Ando effect. The results indicate that selection functions affect the EW0 scale factor. Taking these effects into account, we find that our w(0) values are consistent with those in the literature within 1 sigma uncertainties at 2.9 < z < 6.6 at a given threshold of M-UV and LLy alpha. Interestingly, we find 12 objects with EW0> 200 angstrom above 1 sigma uncertainties. Two of these 12 LAEs show signatures of merger or AGN activity: the weak Civ lambda 1549 emission line. For the remaining 10 very large EW0 LAEs, we find that the EW0 values can be reproduced by young stellar ages (< 100 Myr) and low metallicities (less than or similar to 0.02 Z(circle dot)). Otherwise, at least part of the Ly alpha emission in these LAEs needs to arise from anisotropic radiative transfer effects, fluorescence by hidden AGN or quasi-stellar object activity, or gravitational cooling.