FIG. 1 is a perspective view of a baselayer vest back protector showing our new design; FIG. 2 is a front view thereof; FIG. 3 is a rear view thereof; FIG. 4 is a left side view thereof; FIG. 5 is a right side view thereof; FIG. 6 is a top view thereof; and, FIG. 7 is a bottom view thereof. The portions shown in broken lines show unclaimed subject matter and form no part of the claimed design.