Understanding optical absorption in silicon nitride is crucial for cutting-edge technologies like photonic integrated circuits, nanomechanical photothermal infrared sensing and spectroscopy, and cavity optomechanics. Yet, the origin of its strong dependence on the film deposition and fabrication process is not fully understood. This Letter leverages nanomechanical photothermal sensing to investigate optical extinction κext at a 632.8 nm wavelength in low-pressure chemical vapor deposition (LPCVD) SiN strings across a wide range of deposition-related tensile stresses (200-850 MPa). Measurements reveal a reduction in κext from 103 to 101 ppm with increasing stress, correlated to variations in Si/N content ratio. Within the band-fluctuations framework, this trend indicates an increase of the energy bandgap with the stress, ultimately reducing absorption. Overall, this study showcases the power and simplicity of nanomechanical photothermal sensing for low absorption measurements, offering a sensitive, scattering-free platform for material analysis in nanophotonics and nanomechanics.