Fat babies are healthier, right?

? your kidding right? The physique of a healthy baby is a bit different from a healthy toddler /kid/adult. They have lax muscles that allow a full saggy belly & seem a bit pudgy with soft rolls. That said, there are also fat babies & they are not healthy. You grow new fat cells in infancy/puberty and pregnancy & an overfed fat baby is likely to face a lifetime of avoidable health problems. Your dr can define the limits.
Not always. There is such a thing as overweight even as early as 6 months of age. Some cases involve overfeeding. This is not necessarily healthy at all. Everything in moderation.