Tolkien uses “merry” in its present uses – amusing; jolly – and in a number of its obsolete ones, as musically pleasing, or enjoyable, or boisterous.  I imagine that drawing the line between shades of meaning for the OED must be a complex and very artistic profession.  “Merry” does not appear in Chapters 4, 5, 6, 10, 11, 12, 14, 16.  It’s distributed evenly on both sides of Chapter 10.  I notice that most of the second half “merries” begin here:

[18.019] ‘There is more in you of good than you know, child of the kindly West. Some courage and some wisdom, blended in measure.  If more of us valued food and cheer and song above hoarded gold, it would be a merrier world. But sad or merry, I must leave it now. Farewell!’

I think this is what Richard Blackwelder meant by passages “of great beauty”.  I regard “merry” as a healing word: it’s used by Thorin to heal the rift between himself and Bilbo; it fills the farewells as Bilbo leaves behind his war experience; elves welcome him back to the west with “Merry.”

• 01.051 Quite a merry gathering!
• 01.122 They built the merry town of Dale there
• 02.027 So after that the party went along very merrily,
• 02.028 in merry tales,
• 03.023 talking merrily with them.
• 03.026 and they sang a merry song as the party went across.
• 03.029 and some elves have over merry tongues.
• 03.040 and its merry bells,
• 07.070 in my merry men,
• 08.048 and there was a merry singing,
• 08.058 and laughing merrily.
• 09.025 and laugh merrily.
• 09.039 They had left a merry feast
• 09.044 and make merry
• 09.046 and became mighty merry all of a sudden.
• 09.052 the elves being very merry
• 09.064 and there was a merry racket down by the river.
• 13.034 in merry mood,
• 15.043 and grew merry;
• 17.059 that should have lived yet long ages merrily
• 17.061 and the merry elves.
• 18.019 it would be a merrier world.
• 18.019 But sad or merry,
• 18.042 for now the northern world would be merrier
• 18.044 Merry be the greenwood,
• 18.044 and merry be all your folk!’
• 18.051 and merry there;
• 19.012 Merry is May-time, and merry our meeting.
• 19.012 Merry is May-time, and merry our meeting.
• 19.015 Well, Merry People!’
• 19.018 and he had many a merry jest
• 19.020 Merry is May-time!’
• 19.030 And through the merry flowers of June,

Update 2015.07.09: we discovered further on that “merry” may very well be a not-quite-perfect elf-detector.

Blackwelder, Richard E. Tolkien Phraseology: A Companion to A Tolkien Thesaurus Tolkien Archives Fund, Marquette University, 1990. Print.

“merry, adj.” OED Online. Oxford University Press, March 2015. Web. 11 May 2015.