There are two specific effects rather than a general one, and the specificity is useful. Obesity is one of the factors that can prevent wounds from healing or slow the process. It increases the risk of infection after surgery. Being overweight can also put tension on stitches, which can make them break open.
Both of those are about surgical wounds: infection risk after an operation, and mechanical strain on a closed incision. That is narrower than the way the subject is usually discussed.
In other wounds, weight is one factor among several rather than a verdict. Obesity is one of the risk factors for venous ulcers, alongside varicose veins, a history of blood clots in the legs, blockage of the lymph vessels, older age, being female or tall, family history, pregnancy, smoking, long periods of sitting or standing, and serious leg injuries. In self-care advice for venous ulcers, ischemic ulcers and pressure sores alike, losing weight if you are overweight appears in the same list as quitting smoking, controlling blood sugar if you have diabetes, exercising as much as you can, eating healthy foods, getting plenty of sleep, and managing blood pressure and cholesterol.
That context is worth keeping. A list of ten contributing factors is a different thing from a single cause, and wounds that are slow to heal usually have more than one reason behind them. Working out which reasons apply is one of the jobs of a wound care team: to determine why the wound is not healing.
There is no set weight, target or timescale to reach before a wound can be treated. The measures above may improve blood flow and aid healing in someone who already has a wound. They are offered alongside treatment rather than as a condition of it.