Meaning
Deeply satisfying and pleasing — literally 'sweet to the belly'. Said above all of food that is thoroughly delicious and filling, leaving you contented, it stretches by extension to anything that brings deep, warm satisfaction. Since 'belly' is the plain word for stomach and so much Jamaican feeling about wellbeing turns on the belly being full and happy, 'sweet to di belly' names not just good taste but the whole glow of being well fed and pleased, satisfied right through.
Examples
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Dat pot a rundown did sweet to di belly.
That pot of rundown was thoroughly delicious and satisfying.
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A good day's work weh done well sweet to di belly.
A good day's work done well is deeply satisfying.
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Har cooking always sweet to di belly.
Her cooking is always deeply satisfying.
Origin
Extends 'sweet' (which in Patois means delicious or pleasing, not just sugary) to the belly — the seat of satisfaction — for something that satisfies to the core.
How it’s used
Chiefly of food, but used of anything deeply satisfying. Note 'sweet' in Patois means tasty/pleasing generally.