SHBG (sex hormone-binding globulin) is a protein that binds and carries sex hormones — including testosterone — through the bloodstream.
Obesity lowers SHBG, which in turn lowers measured total testosterone. In some men that's mostly a lab effect and free testosterone is still normal, but obesity can also dampen the pituitary's LH signal and lower testosterone for real. That's why doctors check free testosterone in men with obesity (Anawalt et al., JAMA, 2026 (external link)), and why weight loss often raises the number. See the guide on HRT for men and GLP-1 medications.