Concept:This sentence uses a concessive pattern, where "may" admits a fact before a contrasting idea is given.
Explanation:The sentence shows a contrast between being fat and being smart.
The word needed must introduce a concession, not ability or mere possibility.
The pattern "may + verb + but" is used for this meaning.
Thus, "He may be fat, but he is still smart" is correct.
"Can" implies ability, "could" implies past possibility, and "might" implies weaker possibility, so none fits the concessive structure as well as "may."
Answer:A. may