@Silverhand
Hi! So both of my sons were/are breastfed. My first was a very very fat baby (he just turned 2 and is no longer fat - the fat goes away) and we never had any issues with weight gain. I gave him baby food around 8-9 months, and then it was pretty sparingly. I wasn’t against it, but I really just didn’t see a need to give him baby food when he was so clearly thriving with breastfeeding. I also did not want to give myself the extra work of making or preparing baby food if it wasn’t necessary. Mostly what I did was just hand him pieces of fruit to gnaw on, and he sort of went from breastfeeding to eating real food. I think it had an “official name” - I think it’s called baby-led weaning. That may be a good solution.
Your doctor advised pumping because it’s a good way to measure how much milk the baby is getting. Your baby would still be getting the nutrition of breast milk, so it’s not a total loss. However, the intimacy is much higher for the Mom and baby if breastfeeding continues, and your wife may be really attached to this and may not be wanting to sever or displace the lovely bond.
Have you considered just forgetting baby foods for a while? Your baby won’t suffer nutritionally without them.
The only other reason I could think of for your son not gaining weight would be if the breast milk was inadequate. My cousin had to switch to formula because her son was woefully underweight. Once he started formula he immediately plumped up and grew. But they knew early on -like 3 months old - that something was wrong, and it sounds like that’s not the case with you.
Hope some of this helps!