More specifically, is there a historical reason why some katakana characters look similar to the hiragana ones, as the question suggests?
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Comments are not for extended discussion; this conversation has been moved to chat. – Flaw♦ Jul 11 '18 at 5:54
It is just a coincidence. As you (probably) know, both hiragana and katakana came into existence as shorthand for kanji. Here's the graph shown on Wikipedia. So you can see that ラ and う are derived from different kanji and just so happen to look similar.
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To expand on this note, Japanese had no written form until the Chinese writing system was adopted via Korea, and writing was done by translating the Japanese into classical Chinese; this was until the use of Man'yougana, which was a syllabary consisting of kanji used to represent associated sounds (often more than one kanji per sound); this led to hiragana, whose shapes were based on the overall shape of a particular kanji, and katakana, whose shapes were based on the shape of a component of the same kanji. – archaephyrryx May 24 '17 at 22:05
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There is also the issue of Joudai Tokushu Kanazukai, distinctions between two classes of manyougana that distinguished a number of sounds, but the distinction was lost when manyougana stopped being used in favor of kana, which did not differentiate between the two classes of sound. – archaephyrryx May 24 '17 at 22:09
