Bone marrow mesenchymal stem cells (BM-MSCs) are promising candidates for regenerative medicine purposes. The effect of obesity on the function of BM-MSCs is currently unknown. Here, we assessed how obesity affects the function of BM-MSCs and the role of endoplasmic reticulum (ER) stress and the unfolded protein response (UPR) therein. BM-MSCs were obtained from healthy donors with a normal (<25) or high (>30) body mass index (BMI). High-BMI BM-MSCs displayed severely impaired osteogenic and diminished adipogenic differentiation, decreased proliferation rates, increased senescence, and elevated expression of ER stress-related genes ATF4 and CHOP. Suppression of ER stress using tauroursodeoxycholic acid (TUDCA) and 4-phenylbutyrate (4-PBA) resulted in partial recovery of osteogenic differentiation capacity, with a significant increase in the expression of ALPL and improvement in the UPR. These data indicate that BMI is important during the selection of BM-MSC donors for regenerative medicine purposes and that application of high-BMI BM-MSCs with TUDCA or 4-PBA may improve stem cell function. However, whether this improvement can be translated into an in vivo clinical advantage remains to be assessed.