This is a question scientists are trying to answer. Several long-term studies have been done comparing obese to nonobese patients who have a total knee replacement (TKR). The results aren't always clear.
Obese patients tend to have lower activity levels. This may counter the negative effects of excess weight on the new joint. On the other hand, in some cases, obese patients have been able to increase their activity once the pain is gone. Weight loss becomes possible
Even without any weight loss, obese patients may get enough pain relief and increase in function to make it worth having the operation, even if it doesn't have a perfect result.
A recent study reported results in obese patients 15 years after a TKR. There were more failures in this group compared to the control (nonobese) group. But the failures didn't occur until after 14 years with the joint replacement. Most joint implants are only expected to last 15 years, so this result may not be so unusual.
Your aunt may do very well if she is in good health.