Salt will retain water in your body and thus the weight increase. It is a good thing however, exercise will get toxins out through sweat. I take 15 drops of Lugol's everyday. I do not experience any of these symptoms so could not tell you more. There must be a difference in taking straight Iodine vs. tablets.
You could reduce the salt push to once a day and see if has any benefits. You may be ingesting too much salt. How much salt do you put in one glass of water? Also try Iodine in the morning and salt and vitC in the evening.