In the presence of a constant gravitational force, constant mass implies constant weight. Weight has nothing to do with density. Nothing. None.
Boyance is a separate issue from weight.
EDIT: quoted for great justice
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You have to heat the liquid with solutes up more to get the vapor pressure in it to equal the atmospheric pressure, so it has a higher boiling point.
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from above.
The boiling temperature increases. High school chemistry tells us that solutes increase boiling point and lower freezing point. That's why cooks put salt in their water when they're boiling stuff, and why homeowners go out and buy bags of salt for their driveways.