You might want to take a look at The Universal History of Numbers: From Prehistory to the Invention of the Computer by George Iffrah (your library might have it) for a detailed history of our and other number systems. But to be honest, in all the books on the history of mathematics I've read, not a single author has addressed your question. I assume that the similarity is hence (at least believed to be) coincidental. There is also a good argument to be made for this claim: Our notation derrives from arabic and indian numerals, as you probably know -- Encyclopedia Britannica has a neat picture. The notation of numbers evolved over time, and as you can see, 6 and 9 did not look very similar in the beginning, but became more and more similar over time, e.g. in West Arabic writing, where the symbols were already very similiar, but not yet identical. You can also see an effort to "unify" the style of the numbers by Dürer in the picture mentioned above, which might have added to the use of the same symbol.

While it's not a question of language, strictly speaking, /r/etymology or perhaps /r/linguistics might be able to help you, or at least direct you to persons or resources who can better answer your question.

Based on the Hindu model, the Arabs developed two versions of numerals, East and West Arabic, of which the East Arabic is now by far the dominant. Our own numeral system is based on the now extinct West Arabic numerals. Their name, Gobar, is Arabic for sand board or dust, referring to the practice of performing calculations directly on the ground or on a board covered with sand (which could be wiped clean when calculations were done). The name is now attached to the early Hindu-Arabic numerals introduced into Europe. The oldest surviving sample of Gobar numerals in Europe is a Spanish manuscript from 976.

Source: Mathematics: From the Birth of Numbers, Jan Gullberg, pp 49-50

You can see the numerals referred to on the first row of this image (wikipedia link).

There are several different examples of the numeral in use in script after this, most resemble something between an uppercase L and an uppercase G.

[Speculation past this point]

Since it eventually became common that the numeral 9 is represented with a descender and 6 with an ascender, it's not too much of a stretch to imagine the characters merging with the spread of the printing press. One simply had to turn the 9 upside down and the character would have the correct ascender and would be recognizable as the numeral between 5 and 7.

Question: Could the history of typesetting be relevant? It seems that being able to re-use letters and just flip them upside down would be convenient.