The measurements are a loaded question and it has to do as much with psychology as anything else. I encourage people to weigh daily but react weekly. This is because your weight can fluctuate dramatically from day to day due to shifts in water balance and not necessarily due to gaining fat or losing muscle. Gaining muscle is an extremely slow process so when you read someone gained 5 pounds in a week, more likely they are retaining water which is not fat. Anything that is not fat is referred to as "lean mass" so they increased their lean mass. It is often assumed lean mass is muscle ... not true. Lean mass is "everything but the fat."
The reason I'm fine with people weighing daily is so they can see and understand these fluctuations. That way they start to learn how a meal with more salt than they are used to will result in several pounds gained while a day with fewer carbohydrates can result in rapid weight loss but only because of water flushed out of the system. They'll see that weight can fluctuate up and down several pounds and stop worrying about "Oh my gosh did I derail."
It only takes a little math and common sense to realize a lot of fluctations simply can't be fat or muscle. I've dropped 5 pounds on a 10K run. That would be 3500 calories x 5 = 17,500 calories if it were fat, which clearly isn't possible on a 6 mile run. It's water. On the same token, coming in after a weekend of eating and gaining 5 pounds probably isn't all due to fat, unless you managed to somehow overeat 17,500 calories as well.
So you really won't see the average trend unless you look at week after week, but knowing daily is good to see how your body fluctuates. For body fat, I suggest going even longer - 2 to 4 weeks. Unfortunately, while people love to proclaim they are "6.5%" body fat the truth is even the most skilled instructors do not assess fat that accurately. The so-called "precision" devices such as hand-held or scales that use electricity are actually even more prone to error due to shift in electrolyte and water balance (trust me, as a trainer for years I've watched people in all different shapes and levels of fitness use these devices).
You'll often see someone post "I dropped 2% body fat this week" but the truth is that is going to incude a lot of rounding error. The same person might "gain" 1% the next week and suddenly fret their diet/exercise is off when it's just more rounding error. Instead, I'd shoot for looking at body fat as a trend every 2 - 4 weeks which is long enough to have a substantial difference that won't be as subject to error. I'd also highly, highly recommend having a certified/trained instructor measure using calipers. It's far more accurate to look at "20mm of a pinch of skin" and measure the subcutaneous fat consistently than it is to rely on an electric current passed through your body, especially as you become more fit and lean.
