As a trainer, I track different things for different client goals. I have my clients track different metrics given their different goals.
Weight: Since scale weight is the gross total of your entire mass - fat, muscle, bone, water, that bowl of oatmeal you ate before you came to the gym, etc. - it's a rough measurement. Easy to take, but it doesn't drill down to the specifics of what it consists of. So I'm not generally interested in that for clients interested in fat loss. We'll measure it because it helps us calculate body fat.
For example: A client weighs 145 on day one. On day sixty, the client weights 135. Is that progress towards healthy weight loss? Maybe. But what if the client is dehydrated on day sixty and lost mostly muscle mass due to poor diet choices? We don't know, so it's only part of an answer.
For a client interested in getting bigger and stronger, this is a critical number. Seems odd - the skinny guy who wants to put on mass, the weak woman who wants to get stronger - why is weight more important to them than the person trying to lose weight? Because how much you weigh tells you how much bigger you're getting and provides a number to compare to your lifts.
For example: You pulled 315 at 190, and two months later you pulled 315 again. Are you stalled out? Maybe. But what if you're 185 two months later? Your proportional strength went up. Doing 12 dead-head pullups at 135 is impressive; doing 15 when you are still 135 means straight-up progress.
Body Fat: Now we're getting somewhere. Even if we're using a fairly inaccurate method, as long as it's consistent, it can give us insight into the ratio of lean body mass vs. fat.
For fat loss clients, I will strenuously argue for body fat measurements. The goal is really not weight loss, it's fat loss.
For example: A client drops from 220 to 210 but body fat goes from 25% to 28%. The client has lost more muscle than fat. The client went from 165 pounds of lean mass and 55 pounds of fat to 151.2 pounds of lean mass and 58.8 pounds of fat. That's negative progress - yet the scale says they've made a 10 pound drop!
Waist/Hip Measurements: I do these as waist the belly button vs. widest part of the glutes (other people do them different ways). I find those two are the easiest - check across the belly button, move the tape measure until you find the widest part of your glutes.
These measurements tell us a lot - are you gaining or losing midsection size (and therefore most likely fat)? Are you gaining or losing at the glutes? This is a great measure for folks looking to put on mass, too.
For example: A client's weight stays steady at 200, but the client's waist and hips go from 38" and 42" to 36" and 41.5". The client is most likely losing fat mass, especially around the midsection.
Caliper Measurements: I have not meant a single client who was willing to do these. Not one. I've got a pair of calipers and trained to use them, but used them in the field zero times. Fat loss clients are too embarrassed most of the time, it can feel invasive ("Hi, you just met me, can I use a pair of calipers on your flab?"), and I don't get any bodybuilders or people who need their fat levels drilled down to "but where do I need to lose it?"
Calorie Counts: I've written before about how I generally dislike calorie counting - too fiddly, inaccurately specific ("I ate 1,498 calories today and burned 1,520 calories!" = within +/- 10-20% of each of those numbers), hard to sustain. But in some cases I'll have clients track them to use as a minimum - to ensure they are eating enough. For fat loss clients, I care about food quality and eating consistency, not calorie counts. I know a lot of people swear by calorie counting and can point to success. I've read books by people who've tracked calories every day for years. But I've seen too many clients - in fact, almost all clients - eventually stop tracking, or track obsessively to the point of ignoring clear issues to meet calorie counts.
BMI: I only use body mass index when tracking it for a client that needs to reach a specific BMI for testing purposes. I think it's a useless measure at best. Yes, your height matters, but when lean and strong athletes rate as "obese" and skinny folks carrying a lot of fat are "healthy" you've got a measurement that tells you nothing useful about the client.
Here are some examples.
Case one is a skinny teenage boy looking to get bigger and stronger. He's lifting six days a week, getting in sufficient sleep and recovery.
We track calories, if possible - if not, simple food journaling or recall will do. Ideally we'll have a minimum calorie count each day. We track weight gain, but specifically do not track body fat or waist measurements. Knowing his weight is going up means we know he's putting on body mass. Some will be fat, yes, but most of it will be muscle given his training and eating. Tracking body fat would be useful but distracting - instead of worrying about getting enough food, sleep, and training, the client will also be thinking "Is this good weight? Am I putting on too much fat?" Since the answer is likely no, it's just more mental stress for no good purpose.
Case two is a middle-aged female looking to lose body fat. She's training two-three times a week and stays fairly active, but lack sufficient sleep due to job stress and hours.
We track weight in order to track body fat. We specifically do not track calories, although I may sit down and calculate them vs. a food recall journal and ask the client to add or subtract food from certain typical meals. We track body fat, and if the client agrees (many don't), waist and hip measurements. During discussions I never talk overall body weight.
Note these do rely on clients agreeing to regular measurements - I've had clients who won't let you check anything they can't show improvement on. No getting on the scale unless they've checked before they came and saw it went down (even if the goal is otherwise). No body fat measuring because it might be bad. No waist/hip measurements because it's embarrassing (and they won't do it themselves.) In those cases, I find it's best to ignore the less helpful measurements - don't check weight at all, for example. Instead, work steadily on making progress on processes, and if possible work towards getting useful measurements. Suggest the measurement methods and refer them out to someone else to check, or have them check themselves. It's always going to be more helpful the more information you know, but in my experience it's less than helpful to track, say, weight even though you know it's not giving you good information.