1st. The depth meter indicates that the depth of the defect is about one millimeter, i.e., well below the 1/16 inches (1.6 mm) you mention.
2nd. Is that beam a hot rolled one made according to ASTM A 36? In that case, take a look at the standard, which will tell you the allowable depth of defects.
Or was beam fabricated with welded plates? In that case, knowing what plate was it (ASTM A 283, for example), take a look at the standard, which again, will tell you the allowable depth of defects.
3rd. If I were you, I wouldn't be that much concerned. Looking at the photos, it's evident that the defects are superficial ones. I wouldn't care about the minors and would repair by welding the deeper ones.
Giovanni S. Crisi
Sao Paulo - Brazil