"Embarrassed" is absolutely the right choice. The relevant meaning of "embarrass" according to MW is
"to cause to experience a state of self-conscious distress"
What causes the child to feel distress is not specified in the clause where "embarrass" is used. In other words, the causative agent is not the grammatical subject of the verb and consequently the passive voice is called for. Of course, we know vaguely what the cause is because the clause is introduced with "because." That tells us that the cause is related to his being overweight, but notice that it is not very specific. Is the child mocked for his weight? Does he merely fear being mocked? Does he fear silent contempt? We do not have any deep insight into what causes the child a feeling of distress. We know only the result, and that is what the passive voice gives us.
The problem with this as an example of the distinction between the present participle and the passive participle is that the usage of the word "embarrass" is not strictly logical. In the sense of causing self-conscious psychological distress, the act in truth is necessarily reflexive. We are distressing ourselves. But English almost always treats the cause of embarrassment as something divorced from the "real self."