The answer is historical. In Old English, voiced and voiceless fricatives were phonologically equivalent. (The current English graphemes <v> and <z> did not exist in Old English.) Between voiced segments, voiceless fricatives became voiced--and this is called sibilant softening. Then, in Middle English, these fricatives became phonemic. That's why you see these discrepancies. Words with <s> between voiced segments after the Middle Ages don't fit in this pattern. That's why lousy (from the 14th cy) got /z/ (softened /s/), whereas mousy (from 1853) got /s/.
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.
Best Answer
Apparently, Early Modern English had a four-form system of yes and no, where yes and no were used to answer negatively phrased questions (e.g., "Will he not go?") whilst yea and nay were used to answer positively phrased questions (e.g., "Will he go?"). Since the sort of questions voted on by assemblies are positively phrased, I'd imagine that the legislative use of yea and nay is a relic of this earlier usage.