We almost have a golden word (I just made that phrase up), a word that appears in every chapter. Missing Chapter 15. Germanic probably direct from PIE. The OED has a fabulous article on its etymology

• 1.001 with nothing in it to sit down on or to eat:
• 1.010 sit down
• 1.010 Then Bilbo sat down on a seat by his door,
• 1.043 I really must sit down for a minute
• 1.043 while the four dwarves sat round the table,
• 1.046 The poor little hobbit sat down
• 1.060 Gandalf sat at the head of the party
• 1.060 and Bilbo sat on a stool at the fireside,
• 1.088 and sat down
• 1.088 and sat
• 1.093 as they sat down again.
• 1.124 sat and wept in hiding,
• 1.140 If you sit on the door-step long enough,
• 1.141 and isn’t sitting on the door-step your job,
• 2.002 In fact he was just sitting down
• 2.036 There they all sat glum
• 2.043 Three very large persons sitting round
• 2.080 sitting by them,
• 2.080 or just sit on them one by one
• 2.092 until at last they decided to sit on the sacks
• 2.093 “Who shall we sit on first?”
• 2.094 “Better sit on the last fellow first,” said Bert,
• 2.095 “But if you wants to sit on the last one,
• 2.095 sit on him.
• 3.033 or just sitting
• 4.025 sat a tremendous goblin with a huge head,
• 5.002 but sat down on the cold floor
• 5.014 while Bilbo was sitting on the brink
• 5.022 Praps ye sits here
• 5.022 with other funny creatures sitting
• 5.045 and sitting under the river bank teaching his grandmother,
• 5.047 since you are sitting comfortably at home
• 5.047 Bilbo sat
• 5.053 two-legs sat near on three-legs,
• 5.054 man at table sitting on a stool,
• 5.056 Poor Bilbo sat
• 5.058 He sat down
• 5.060 with that nasty wet cold thing sitting next to him,
• 5.078 He sat still,
• 5.112 Suddenly Gollum sat down
• 5.126 There was Gollum sitting humped up right
• 5.136 with drawn swords sitting just inside the door,
• 6.019 and he sat down
• 6.020 with him sitting beside me,’
• 6.020 And then he sat down
• 6.028 and there he sat down
• 6.052 if you had seen the dwarves sitting up
• 6.052 and were trying to find a place to sit
• 6.059 Trees are not very comfortable to sit
• 6.060 went and sat
• 6.066 He was sitting,
• 6.071 Some of them actually sat down
• 6.090 said Bilbo sitting up
• 6.093 sitting with their backs to the mountain wall.
• 7.001 So he sat down
• 7.023 I once saw him sitting all alone
• 7.046 Here they sat on wooden benches
• 7.066 Sit down,
• 7.070 and then sit down
• 7.071 and sat flop on the floor looking rather surprised.
• 7.078 Sit down
• 7.082 and sit down!
• 7.088 Now he had got fifteen strangers sitting
• 7.093 low enough even for Bilbo to sit at comfortably.
• 7.093 (in which he sat
• 7.093 What did the rest sit on?
• 7.096 They sat long at the table
• 7.096 and still they sat
• 7.097 The dwarves were sitting cross-legged on the floor round the fire,
• 7.117 ended Gandalf, and he sat a long while silent.
• 7.133 or sitting at noon
• 7.136 or sitting far off
• 7.146 Bilbo sat on the ground feeling very unhappy
• 8.006 and sat at night
• 8.032 and as they sat
• 8.033 There they sat for a long while
• 8.047 and sat up scratching his head.
• 8.048 he sat down
• 8.058 and sitting on sawn rings of the felled trees
• 8.071 sat a woodland king with a crown of leaves upon his golden hair,
• 8.074 So he sat himself down with his back to a tree,
• 8.081 and horrible sitting
• 8.093 and taking off the spider sitting
• 8.126 He just sat staring
• 9.002 and sat down
• 9.005 sat the Elvenking on a chair of carven wood.
• 9.017 He sat and thought
• 9.021 For some time Bilbo sat
• 9.025 and sat down at a table on which two large flagons were set.
• 9.034 and you can sit there comfortably
• 9.063 and the trail of drippings that he left wherever he went or sat;
• 10.012 where they sat or lay muttering
• 10.030 who were sitting
• 10.037 and crowds sat outside
• 11.020 Bilbo found sitting on the doorstep lonesome
• 11.020 when he said they could sit on the doorstep
• 11.020 And sit
• 11.021 He would do nothing but sit with his back to the rock-face
• 11.022 You said sitting on the doorstep
• 11.022 so I am sitting
• 11.027 just above the enclosure where he was sitting –
• 11.028 All day Bilbo sat gloomily
• 12.082 The old thrush was sitting
• 12.091 and I don’t see the point of sitting here.
• 12.094 So for a longish while they sat inside
• 12.098 He sat nearest to the door
• 13.001 the dwarves sat
• 13.001 but they could not sit there for ever.
• 13.015 and they sat huddled
• 13.017 So they sat near the door
• 13.039 and sat down on the floor;
• 13.052 where we can sit quiet for a bit!’
• 13.071 but the others sat near the outer door
• 14.037 and remained sitting on the ground.
• 16.025 Bilbo was sitting beside a warm fire
• 16.025 and there sat too,
• 16.027 he is quite ready to sit on a heap of gold
• 16.027 as long as you sit here.’
• 16.042 rose from a tent door where he was sitting
• 16.046 and then he sat down on the wall
• 17.033 But who are you that sit
• 17.060 sitting on the ground as if
• 18.003 He sat up painfully.
• 18.007 not far from where Bilbo sat.
• 18.017 to sit beside my fathers,
• 18.020 and sat alone wrapped
• 19.041 Bilbo was sitting