Why is “mwy” used in " were they expecting to eat more than me" but “yn fwy” is used in “we weren’t relaxing more than you?”
Dunno - maybe some grammary types will be able to help when they notice this - but in broad terms, most ‘why’ questions really boil down to ‘because languages work differently’ - so ‘more’ is the same word whether it’s working like a noun or an adverb in English, but in Welsh not so much… 
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Because in the first one mwy is the object of the verb, so really equivalent to a noun, while in the second one it’s an adverb, describing the action of the verb itself relax.
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It is because some words have a ‘soft mutation/treiglad meddai’ after the ‘yn’ link word. Mwy is one of those words and ‘m’ mutates to ‘f’, hence mwy becomes fwy after yn.