There are various theories regarding the original meaning of the Balch name. Below are three possible descriptions of what the name might mean.
1. English: from Middle English balch, belch ‘balk’, ‘beam’ (Old English bælc, balca), possibly denoting someone who lived in a house with a roof beam rather than in a simple hut; alternatively it may have been a nickname for a man built like a tree trunk, i.e. one of stocky, heavy build.
2. English: nickname from Middle English balche, belche ‘swelling’ (Old English bælc(e)). This was probably chiefly given in the sense ‘swelling pride’, ‘overweening arrogance’, but it can also mean ‘eructation’, ‘belch’ and may therefore in some cases have been acquired by a man given to belching.
3. Welsh: from the adjective balch, which has a range of meanings—‘fine’, ‘splendid’, ‘proud’, ‘arrogant’, ‘glad’—but the predominant meaning is ‘proud’ and from this the family name probably derives.
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4
In Galusha Balch's book, Genealogy of the Balch Families in America, he discusses records of individuals with the Balch name and the very real possibility of variations to the name:


Definitions:
A dictionary of the Welsh language: explained in English; with …, Volume 1 By William Owen Pughe
Surname: Boakes
This name, with variant spellings Baulch, Belch, Belk, Boakes, has two distinct possible origins, the first being a metonymic occupational name for someone involved in the erection of roof-beams. The derivation in this case is from the Medieval English "balch" or "belch", itself coming from the pre 7th Century Old English "balca", a balk or beam. The word may also have been used metaphorically for a man of stout, heavy build. The second possibility is that the name originated as a nickname from the Medieval English "balche" or "belche", literally meaning "swelling", but used chiefly in the sense of "swelling pride" or arrogance. Early recordings include: William le Belch, (Essex 1295); Robert Balch, (Somerset, 1327) and Richard le Balch, (Sussex, 1332). In 1604, one, John Balche was entered in "The Oxford University Register", and on November 26th 1637, William Balch and Mary Browne were married in St. Helen's Bishopsgate, London. The first recorded spelling of the family name is shown to be that of William Belch, which was dated 1185, "The Knights Templars Records of Oxfordshire", during the reign of King Henry 11, known as "The Builder of Churches", 1154 - 1189. Surnames became necessary when governments introduced personal taxation. In England this was known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.
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Primary Sources/Links:
SurnameDB: Boakes Surname Meaning
Balch Families Living in England and Wales in 1891 - Ancestry.com
Possible Sources - All Mentioned by Galusha Balch:
The chronicle of Battle Abbey, from 1066 to 1176 - By Mark Antony Lower
English surnames and their place in the Teutonic family - By Robert Ferguson
English surnames: their sources and significations - By Charles Wareing Endell Bardsley