Saltwater does kill weeds, and it does this by traveling up through their roots and dehydrating the plant as it is absorbed. Like vinegar, salt water is also non-selective, which means it will harm all the plants it comes into contact with. To effectively use salt water as an herbicide, use a 3:1 mixture of water to salt and use a funnel to pour it directly on each weed, then water the surrounding plants to mitigate damage.
Saltwater should be used sparingly in your lawn, as salt is not biodegradable. Instead of breaking down, salt builds up in the soil and can change the pH, eventually eliminating necessary nutrients from the soil and making it impossible for anything to grow.