It's recommended that you weigh yourself once a week, first thing in the morning after peeing. Our bodies' weight fluctuates during the day, week, etc. so it's best to just weigh once a week, usually the same day.
Your other question, I don't know anything about the Fuel Band. I have a BodyMedia Armband and it tells me what I burn during my workouts (what it considers exercise) and the total calorie burn for the day. I do know that it will show that I exercised longer than I did if I get too hot. One day this week, I had on three shirts and a jacket and it said I'd exercised for 429 min (I knew that wasn't true), so I subtracted that amount from my exercise total. If you can tell what you burned before exercise and after, then take the difference and enter it in the Fitness section.