My 2 month old son eats 4-5oz of formula every 2 hours during the day. when should he start eating more or how long should be keep eating this amount?

Depends on age & wt: Most infants will tend to increase their intake over the first few weeks and then level off between 28-35 oz/ 24 hours until they weigh about 15 pounds, and then additional intake is needed. For most babies, this is usually around 4-6 months, so solids are added then. Some 2 month old infants will take 7 oz x 5 bottles a day, others 4 oz x 8/ day. If your baby is happy and growing, no worry.