At what age can a child start lifting weights like barbells or dumbbells?

See below. The important thing with weight training in children is proper technique. They will not develop increase in muscle mass, until puberty.
Depends on type. Strength training is ok an any age under the guidance of qualified trainers. The growth plates in the long bones are not as strong as ligaments, so little johnie playing conan will fracture a growth plate before he sprains a ligament.The aap recomends a kid be at stage 5 (end) of puberty before involvement in power lifting or other such events. If shaving daily, stinky & <1in from final height, ok.