I wish to write a sentence to ask:
How does the weight of a car
affectthe speed of it?
Should I have
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In any clause no more than one verb† can be inflected for tense, person and number, and that one verb must be the first in the chain.
In your example the first verb in the chain is the auxiliary do, and that is inflected; auxiliary do always takes an infinitive as its complement, so affect is what you want.
†Except in cases where two or more inflected verbs are conjoined with and or but or (n)either..(n)or. Here the conjoined verbs co-occupy the same syntactic position and role, so the "rule" holds.