I think it may also have something to do with being respectful. There are actually three "you"s. The first is Aap and is the highest form of respect. The second is tum and is what is used normally. And the third is Tu, which would mostly be used with people you are very close to. I think that when picking the corresponding verb, you would use the plural form if you wanted to show more respect.
Like आप, तुम always behaves as if it were plural regardless of how many people you're talking to, so you say तुम पढ़ते हो (male) or तुम पढ़ती हो (female) but never तुम पढ़ता हो. It's common to stick on लोग ("people") when addressing multiple people, e.g. आप लोग (formal) or तुम लोग (semi-formal).
हे he: never
हूँ hum/hung: only with मैं main (I - 1st person singular)
हो ho: only with तुम tum (medium-formal you)
है hai: with तू tuu (very informal you), वह/यह vah/yah (he/she/it/this/that), any singular person or object
हैं hain: with हम ham (we), वे/ये ve/ye (they/those/these), आप aap (very formal you), any plural objects or people
"तुम (tum) is the mid level formal way of expressing "you" in Hindi and is used when addressing those of equal social status or those one has a close enough relationship with to justify the reduced formality.
Because the less formal forms could offend others, आप (āp) is the safest way to express "you" unless there is reason to be less formal. Because तुम (tum) is grammatically plural (adjectives and verbs etc affected by it take their plural forms) even when there is only one person being referred to, the term तुम लोग (tum log) (literally: you people) can be used to specify that more than one person is being referred to."
So normally तु (tu) is the second person singular (equivalent to Latin 'tu' and English 'thou' or German 'du'), but as तुम (tum) it is singular in meaning, but plural in grammar, just like English 'you' (the polite form of 'thou', rather than 'you' as plural second person). The same can be seen in German with 'Sie' as the polite form, but 'ihr' = 'you' in plural.