I personally do weekly progress pictures if they will allow you. If you cant get them to cooperate at all then by the process of you working out with them you can be performing assessments on them that are time or rep based.
You could also measure their heart rate throughout and show the drops or increases and the duration they are able to be held for.
I believe by them seeing the results of your training on paper they will be more willing to allow more intrusive ways of measuring to take place. Especially once you explain the importance of knowing their BMI, how many inches they’ve lost, their body fat, heart rate training zones, obesity classification, fat and lean mass.
I hope that helped!
Good luck to you