How to analyze "dearly beloved"?

Solution 1:

Beloved seems to be either an adjective or a past participle acting as a noun.

This use is similar to "the fallen" to mean the people who have died. To modify this phrase, we have two options: (1) modify the noun derived from the participle by adding an adjective, or (2) modify the participle by adding an adverb and then make the whole phrase into a noun.

1) Recent fallen - "fallen" is essentially a noun phrase, but a one-word phrase because we've elided a word. "Fallen" is essentially fallen people. We can modify the whole noun phrase (fallen people) by adding an adjective. Thus, recent fallen -> recent (fallen people) -> fallen people who are recent.

2) Recently fallen - if we use an adverb instead of an adjective, we must be modifying the participle, rather than the noun phrase. Recently modifies fallen, not fallen people. Thus, recently fallen -> recently fallen (people) -> people who have fallen recently.

Likewise with beloved. We can modify the noun: dear beloved. This would describe beloved people who are dear.

We can modify the adjective/participle: dearly beloved. This would describe people who are beloved dearly.

Solution 2:

A complementary answer:

I thought adverbs could only modify verbs or adjectives?

The categories "adjective" and "adverb" are very fuzzy in English. Words that can be used indiscriminately to modify any other word—nouns, verbs, adjectives, adverbs, prepositions even—are probably more common than words that can only modify some categories of word.

It's true that we have the -ly suffix that you have to apply to some (but not all) "adjectives" when you want to use them to modify verbs and other modifiers, and remove from some (but not all) "adverbs" when you want to use them to modify nouns. Calling this suffix a derivation operator that "turns adjectives into adverbs" is, I think, a relict of If-only-English-were-Latin grammar theory. If we were working up a descriptive grammar of English from scratch, I suspect it would be cleaner to have just one category of "modifier," and treat the -ly suffix as an agreement marker, instead of an operator.