Does this "may already have been" denote a past tense or a past perfect tense? Does "may have pp" change depending on the subject's tense like the following?
ex)I think he may have come => I thought he may have come(or he might have come)?
2)There are a number of causes of childhood obesity, but researchers have been considering the effects of TV advertising for years...They also took steps to account for the possibility that some children may already have been overweight and inactive regardless of their TV-watching habits.
'May' can never be used to form a past perfect tense.
Since reference here must be to the situation prior to that denoted by the main verb (a past tense 'took'), 'might have been' would clearly be the more appropriate choice.