I lost a significant amount of weight 10 years ago-to the point where it was hard to believe the guy in the passport picture was me. I carried the passport with that photo for about three years. During that time I always got second and third looks from inspectors along with questions about the weight loss. On occasion I was asked to provide a second form of ID. Fortunately my drivers license had an updated picture. I was never refused entry because of the outdated photo in the passport. I cannot say what would’ve happened in those cases where I was asked for the second ID were I not to have had one. I’m sure something would have been worked out though.
Keep in mind many people significantly change in appearance due not only to weight loss but to illness as well. I’m sure border inspectors see many of these cases daily.