From a Scouting resources site
A piece of kelp or seaweed hung up will become damp previous to rain - Any truth probably comes from salt remaining on the surface of the weed. Salt is hygroscopic, which means it will absorb moisture when the air is humid. This may mean the chance of rain is slightly higher. Sailors noted that ropes tend to be harder to release ahead of rain (they shrank). Musical stringed instruments sound as tension increased due to shrinking. Rush matting was found to shrink in dry and expand in hot weather.
So you see, you don't need any seaweed - you can do exactly the same thing with a banjo. There, got it back to music!