The Oxford dictionary of word orgins supplies:
chuck L16th
This informal word meaning ‘throw’ is the same as the one meaning ‘touch (someone) playfully under the chin’, probably from Old French chuquer, ‘to knock, bump’ (of unknown ultimate origin). The chuck [L17th] of a drill is a variant of chock, with chunk [L17th] another variant. The phrase the chuck expressing rejection (give somebody the chuck) dates from the late 19th century, while the sense ‘to vomit’ is an Australianism from the mid 20th century.
The OED supplies one usage from L16th:
1593 Prodigal Son iv. 112 Yes, this old one will I give you (Chucks him old hose and doublet).
This example cited in many books, including Slang and its analogues past and present.
The text of the play is found in: The school of Shakspeare (1878).
The Concise Oxford Dictionary of Etymology says:
Chuck
give a playful touch under the chin; throw with the hand XVI.
Also (dial.) chock XVI. perh. — OF. chuquer, earlier form of choquer knock, bump, of unkn. orig.
Wheat's An Etymological Dictionary of the English Language (1898) has an entry for chuck and states that the word is a doublet of 'shock', which also comes from Old French choquer. But I didn't find any uses in the OED of 'shock' to mean 'chuck/throw'.
Klein's A Comprehensive Etymological Dictionary of the English Language (1971), p 286 notes:
chuck
tr verb, to throw--From earlier chock, from French choquer, 'to shock', which is probably borrowed from Dutch schokken, a word of imitative origin. Compare shock, 'to collide'.
and
An Etymological Dictionary of Modern English (1921) says:
chuck. To throw. Earlier chock. F. choquer, of doubtful origin. Earliest E. sense is connected with chin.
A definitive answer appears hard to give, anyway to your research I'd add the information offered by The Phrase Finder which has a different story to tell linked to 'pugilism'. Everything considered, to me the tradition to give Christmas boxes with gifts to tradespeople and servants appears to be the most plausible:
'Christmas boxes' were originally literally earthenware boxes. In mediaeval England these boxes were used by the poor (servants, apprentices etc.) to save money throughout the year. At Christmas the boxes were broken open and the savings shared to fund Christmas festivities. This meaning of 'Christmas box' dates back to at least the early 17th century. The boxes were known in France as tirelire and are referred to in Randle Cotgrave's A Dictionarie of the French and English tongues, 1611:
"Tirelire, a Christmas box; a box having a cleft on the lid, or in the side, for money to enter it; used in France by begging Fryers, and here by Butlers, and Prentices, etc."
In a similar tradition, which is almost as old as the above and which is the one that has stayed with us until the present day, Christmas boxes are gifts, usually money, given to tradespeople or others who have rendered some service throughout the year but who aren't normally paid directly by the donor - for example, office cleaners, milkmen etc.
So, why is Boxing Day so called? Sporting fixtures, which used regularly to include boxing, have taken place over the holiday season for centuries. The view that Boxing Day was a day for pugilism gets some support via the earliest reference to the name that I can find, which is in The Sporting Magazine, Volume 25, 1805:
On boxing-day, Dec. 26, a numerous assemblage of the holiday folk were amused by a hard fought battle, in St. Pancras-fields. This fight was one that afforded plenty of diversion to several pugilists and admirers of the art present.
Nevertheless, the link to boxing in that citation is purely co-incidental and the origin of the name is the giving of 'Christmas box' gifts to tradespeople, which traditionally took place not on Christmas Day but on the first subsequent working day.
This article of TIME try to shed some light on its origin:
The best clue to Boxing Day's origins can be found in the song "Good King Wenceslas." According to the Christmas carol, Wenceslas, who was Duke of Bohemia in the early 10th century, was surveying his land on St. Stephen's Day — Dec. 26 — when he saw a poor man gathering wood in the middle of a snowstorm. Moved, the King gathered up surplus food and wine and carried them through the blizzard to the peasant's door. The alms-giving tradition has always been closely associated with the Christmas season — hence the canned-food drives and Salvation Army Santas that pepper our neighborhoods during the winter — but King Wenceslas' good deed came the day after Christmas, when the English poor received most of their charity.
King Wenceslas didn't start Boxing Day, but the Church of England might have. During Advent, Anglican parishes displayed a box into which churchgoers put their monetary donations. On the day after Christmas, the boxes were broken open and their contents distributed among the poor, thus giving rise to the term Boxing Day. Maybe.
But wait: there's another possible story about the holiday's origin. The day after Christmas was also the traditional day on which the aristocracy distributed presents (boxes) to servants and employees — a sort of institutionalized Christmas-bonus party. The servants returned home, opened their boxes and had a second Christmas on what became known as Boxing Day.
So which version is correct? Well, both. Or neither. No one, it seems, is really sure. Both the church boxes and the servant presents definitely existed, although historians disagree on which practice inspired the holiday.
Early citation of 1809:
- from page 321] ... Never alter your dress at this time [the Christmas holidays and boxing- day], but wear the worst of every thing you have; (from Le Beau Monde, or Literary and Fashionable Magazine, 1806-1810Volume 4, No. 30 For January, 1809)
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Best Answer
I found this from googling, so its validity may be questionable, but it came up fairly often.
It seems that both underdog and top dog originated from dog fighting which went on in the 19th century. The losing dog ended up on the bottom, or under the winner, who was on top.
My reference is The Times of India.