Increasingly restricted availability and environmental impact of mineral oils have boosted the interest in sustainable lubrication. In this study, the thickening properties of sodium carboxymethyl celluloses (CMCs) were investigated in order to assess their potential as viscosity modifiers in aqueous gear and bearing fluids. The pressure, temperature and shear dependence of viscosity was studied at different concentrations and molecular weights $M_W$. The tribological properties were investigated at different viscosity grades in both sliding and rolling contact, and compared to rapeseed oil and polyethylene glycol 400. The viscosity of the CMC solutions was adjustable to all application-relevant viscosity grades. Viscosity indices were similar or higher compared to the reference fluids and mineral oil. Temporary and permanent viscosity losses increased with $M_W$. Permanent viscosity loss was highest for high $M_W$ derivatives, up to 70%. The pressure-viscosity coefficients $\alpha$ were low and showed a high dependency on shear and concentration. In rolling contact, low $M_W$ CMC showed up to 35% lower friction values compared to high $M_W$, whereas no improvement of lubricating properties was observed in sliding contact. The results suggest that low $M_W$ CMC has great potential as bio-based thickener in aqueous lubrication.