I bought my eldest a really nice New Balance bat when he was 9... size 5 I think. Used it a for a few weeks before we decided it was way too heavy for him. He's 11 now, not a small boy, and it's still too heavy!
His new bat was from a place round the corner from us in Essex...
Worsop Stebbing.
The advice they gave me was that he should be able to hold the bat out straight in his no-dominant hand without his arm shaking... Having a nice heavy bat is great if you're Chris Gayle or MS Dhoni but for a beginner it's about the worst thing you could do!