Typical yellow, white and red onions have an average sugar content of about 3%. For an onion to be considered "sweet" it should have a sugar content of at least 6%, but some have as high as 15%.
Sweet onions also have a lower concentration of pyruvic acid, which is part of the chemical reaction in onions that accounts for their pungency and the tearing effect produced when cut (see here) . An ordinary onion has a pyruvic-acid content of 10% to 13%, whereas a sweet onion typically has levels below 5%.
Therefore the sweetness as such does not influence the tearing effect.