You also need to address, which you did not mention, his days of rest following each pitching outing. For his age (11) and for next year (12), according to the Pitch Smart guidelines, he will need a full 1 day of rest if he throws 21 pitches in a game; 2 days if he throws 36 pitches; 3 days if he throws 51 pitches; and 4 days if he throws 66 pitches (up to a daily max of 85).
Based on what you wrote, in his tournament this past weekend he averaged 2.1 strikeouts per inning. If he threw 3 innings on Saturday with 6-7 strikeouts, he had to have thrown at least 36 pitches (9 batters @ 4 pitches each). 36 pitches required that he have 2 days of rest (Sunday and Monday). Even if he threw 25 pitches over the 3 innings (unlikely with that many strikeouts), he still would have needed 1 day of rest (Sunday). Instead he got 0 days of rest, pitching the very next day, Sunday. And, if he threw 6 innings on Saturday with 12-13 strikeouts, he had to have thrown at least 72 pitches (18 batters @ 4 pitches each). 72 pitches required that he have 4 days of rest. Instead he got 0 days of rest, pitching the very next day, Sunday. Any way you slice and dice that weekend, he was overused.