These are all interrogative words so there is nothing weird that they all share the same prefix "wh".
And actually there are more than 600 English words that start with "wh", even there is a history for "wh", there won't exist a strong connection between that history and the set of interrogative words.
From Wikipedia:
Early history of ‹wh›
What is now English ‹wh› originated as the Proto-Indo-European consonant *kʷ. As a result of Grimm's Law, Indo-European voiceless stops became voiceless fricatives in most environments in Germanic languages. Thus the labialized velar stop *kʷ initially became presumably a labialized velar fricative *xʷ in pre-Proto-Germanic, then probably becoming *[ʍ] in Proto-Germanic proper. The sound was used in Gothic and represented by the symbol known as hwair; in Old English it was spelled as ‹hw›. The spelling was changed to ‹wh› in Middle English, but it retained the pronunciation [ʍ], in some dialects as late as the present day.
Because Proto-Indo-European interrogative words typically began with *kʷ, English interrogative words (such as who, which, what, when, where) typically begin with ‹wh›. As a result of this tendency, a common grammatical phenomenon affecting interrogative words has been given the name wh-movement, even in reference to languages in which interrogative words do not begin with ‹wh›.
Partridge
Partridge's A Dictionary of Slang and Unconventional English (2002) says:
into (a person) for (a sum of money), be. To owe a person so-much, to have let him down for a stated amount: Can, coll.: late C. 19-20. John Bearnes, Gateway, 1932, He's into me for ninety dollars, and I can't get a cent out of him.'
Where Can coll. is Canadian colloquial. The 2007 edition more simply says:
into preposition 1 in debt to, US, 1893
"... into me for ..."
Diving into Google Books, here's a possible 1902 from the American Ainslee's Magazine, Volume 10, Issues 1-6:
"Old man," confided Bill, after explaining the situation, "I need just a dollar and ten cents. Let me have it, like a good fellow." "But, Bill," replied Reece, hesitatingly, "you're into me for fifty dollars already."
And a definite 1903 from Arthur Morris Binstead's Pitcher in Paradise: Some Random Reminiscences, Sporting and Otherwise, published in London:
Two unplaced's an' one second, an' damme, she was into me for thirty-eight quid ! Stupid ? Aye, laad, even the bloomin' clerk rounded on me !
Here's a possible 1890 in Puck magazine which may be using a with a pun on the phrase:
"You 've got into me for all I 'm worth," remarked the Stocking to the Jumping-Jack. "All the same, I'm in a hole," replied the Jumping-Jack. And when Santa Claus heard them talking in that way, he broke the Jumping-Jack and took the ...
Walked and dribbled
Here's an interesting one from a possibly 1903 Pearson's Magazine:
He has dribbled into me for a thousand if he's had a cent, and now he must pay back by taking a chance.
Dribbling can also be found in the possibly 1917 Norsk-Engelsk Ordbog:
summer little sums ; cont driblets, petty sums. Cold has dribbled into me for a thousand ;
And finally, these two have walked into me for a [sum], which could be part of the same phrase.
Best Answer
Both sets of words come from a Proto-Indo-European root *kʷ(o)- that probably marked an interrogative pronoun. In the Germanic languages, Grimm's Law spirantized this *kʷ into /xw/ or /hw/, which later merged with /w/ in many Germanic languages (Dutch wat, German was, Swedish vad, etc.), though not all: English has what (in some dialects still pronounced with and unvoiced /ʍ/), Icelandic has hvað /kvað ~ xvað/, and Norwegian is probably the silliest, having dialectal and lexical variation between /v ~ kv ~ k ~ Ø/ (the last only before back vowels).
In Latin, *kʷ remained in most words as /kw/ (written ⟨qu⟩), so we have quis, quod, quam, etc. from this root. Cūr is from the same root, but before a high back vowel /u/ the labial element in /kw/ was usually lost in Latin, so early Latin quōr /kwoːr/ (which regularly became quūr /kwuːr/) yielded cūr /kuːr/. Even where Latin kept the labial element in /kw/, though, it usually (though not always) disappeared in the Romance languages, the daughter languages of Latin, leaving just a /k/ as in Spanish que, Italian che, French quand, etc.
In the other branches of Indo-European languages, the development was generally as follows:
Greek: in the largest dialect group, Ionic-Attic, PIE /kʷ/ (mostly) became /t/ before front vowels (τίς tis ‘who’, τί ti ‘what’) and /p/ elsewhere (ποῦ ‘where’). In some other dialects, it (at least sometimes) turned into /k/.
Balto-Slavic: In Slavic it generally resulted in /k/ before back vowels and č /tʃ/ before front vowels (Old Church Slavonic čьto ‘what’, kъto ‘who’); in Baltic generally /k/ everywhere (cf. Lithuanian kas ‘who, what’).
Celtic: It became /k/ in Goidelic (Old Irish cia ‘who’, cid ‘what’) and /p/ in Brythonic and Continental Celtic (Old Welsh pwy ‘who’, pa ‘what’).
Indo-Iranian: In Sanskrit it was mostly generalised to /k/ (कः kaḥ ‘who’, किम kim ‘what’), though it should have yielded /c/ before front vowels; in Iranian there was no such generalisation, and it generally became /k/ before back vowels and /tʃ/ before front vowels (Avestan kō ‘who’, čim ‘what’)
Others: In Hittite and Tocharian, it remained /kʷ/ (Tocharian kus, kᵤse /kʷse/ ‘who’, Hittite kui-/kue-/kuu̯a- /kʷi-, kʷe-, kʷa-/). In Armenian it seems to have been irregularly weakened to /h/, which was subsequently lost: the generalized stem հի- hi- became ի- i-, found in words like ինչկ inč’ ‘what’.
[From StoneyB's comment:] Scots English employed /xw/ at least into the 16th century—and spelled it ‹quh›. See this question.