In an earlier work we introduced a covariant model of quarkonium-glueball mixing and calculated the wave functions of the various mixed scalar-isoscalar and In the present work we introduce the widths of these states and describe glueball mixing with the resonance using a perturbative scheme. Part of our motivation lies in the recent work of Narison who used QCD sum-rule techniques to study the distribution of glueball strength among scalar, pseudoscalar, and tensor mesons. We find little change of our previous results with little strength in the energy region below the resonance. Our result is in contrast to the result of the QCD sum-rule analysis that suggests that there is a good deal of glueball strength in the region near or below 1 GeV.