Oh christ.

That's not a fat baby. Babies are supposed to have a higher percentage of bodyfat (relative to total body mass) at this age. They actually need it for organ development. Unless we're talking a 0-36 month old in the 5th percentile for height
combined with 95th (or higher) percentile for weight, you should actually worry more if your baby/toddler is underweight.
Many normal weight for height kids don't "thin out" until they're close to school age.