The story
Old English had its own word: þēah, ending in a throaty H sound like the ch in German doch — which is a related word, as is Dutch doch. It survived into Middle English as thegh.
But in northern and eastern England, Norse-speaking settlers had a similar word of their own, þó (earlier þóh). In Middle English the Norse-shaped form, written thogh or though, spread and pushed out the native thegh in most dialects. Both forms go back to the same Germanic word.
The gh at the end recorded that throaty final sound. Like the GH in night and daughter, it was lost from speech, leaving a word that is spelled with six letters and pronounced with three sounds: TH-O. The spelling stayed because it was already established before the sound disappeared.
Though is part of the famous -ough family — though, through, tough, cough, bough — whose spellings all once marked the same lost sound, but which ended up pronounced in different ways. The informal spelling tho simply writes down what people actually say.
