Weight gain after starting HIV therapy is common, but recent studies have found that some people with HIV (PWH) who are taking an integrase inhibitor (INSTI) combined with a tenofovir alafenamide (TAF) regimen may gain more weight than people taking other drug combinations. A rising number of PWH are overweight or obese, and a higher body mass index (BMI) increases the risk for diabetes, heart disease and stroke. This study will include PWH who have been virally suppressed on a regimen consisting of an integrase inhibitor (INSTI) and TAF/FTC or TAF/3TC, and have a BMI of 30 kg/m2 (the cut-off for obesity) or greater. This research study is trying to find out if they could gain less weight, or maybe lose weight, after switching to a regimen containing doravirine (DOR) with TAF/FTC (or TAF/3TC), or DOR with the related medication tenofovir disproxil (TDF/FTC [or TDF/3TC]) as compared to continuation of their current INSTI plus TAF regimen.