According to Wikipedia, Pratchett has spent much of his life in the southwestern part of England, growing up in Buckinghamshire, and living in Somerset and Wiltshire. The use of -s in many verb forms (and not just in the 3rd person singular) is a dialect feature in this region.
Peter Trudgill writes in Dialects:
The grammatical rule for present-tense verb forms in the Berkshire dialect is obviously not the same as the one in Standard English. As you can see, Berkshire verb forms have the present-tense -s for all persons. The verbs go like this:
1st person I sings we sings
2nd person you sings you sings
3rd person he/she/it sings they sings
Present-tense verb forms like this are part of the grammatical structure of dialects in many areas of southwestern England and South Wales, as well as other areas.
Like many regional dialects in England, this feature is well along the process of being displaced by the dialect of London and the southeast, but hangs on in the more remote and rural areas.
Pratchett doesn't have a well-worked-out system of dialects in his Discworld novels. Instead, he applies a variety of features somewhat haphazardly to indicate that a character speaks a non-standard dialect. Here are some examples of characters from widely separated parts of the Discworld demonstrating this grammatical feature:
Wintersmith — Granny Weatherwax — ‘I hopes I sees you in good health.’
Small Gods — unnamed Omnian — ‘Listen, I knows a square when I sees one!’
Snuff — Willikins — ‘I knows a bad one when I sees them.’
Interesting Times — Cohen the Barbarian — ‘I knows a wizard when I sees one!’
Pratchett's other techniques for indicating non-standard dialect include eye dialect:
Monstrous Regiment — Sergeant Jackrum — ‘This, my lads, is what we call a real orientation lectchoor...’
Guards! Guards! — Sergeant Colon — ‘We’re jus’ goin’ down, goin’ down—’
And H dropping:
Thief of Time — unnamed dwarf — ‘Sign ’ere, where it says “Sign ’Ere”.’