Yoga is mostly designed for flexibility improvement, though it does have spiritual connotations too.
Expect it's effects on weight loss to be potentially minimal.
Pilaties may have more effects on weight and from what I understand it uses more dynamic movement like limb rotations as well as repetitive movements. I have heard Yoga being claimed to be dynamic exercise, but in fairess, much of it is just static stretching with controlled breathing techniques, with occasional arm, neck or Hip movements. To be dynamic stretching, the movement should be something like Scissor and Pulls, Hip rotations, ankle rotations, Windmills etc. Mimicking a tree until you've done a certain number of breaths is static stretching as is sitting back onto your lower Legs with your head on the floor breathing for a certain number of times and other things like the lotus position as examples. It's semi-dynamic in so much as there are sometimes repetitve neck arm and waist movements, but not in all the moves, the only movement on some moves, being that which gets you into the static position. However I believe Pilaties is more dynamic and involves more movement of the body, so the caloric burning yield should be greater from Pilaties than Yoga.
Yoga has benefits don't get me wrong, but I wouldn't say it's effects on weight loss are greater than Pilaties and Pilaties is not going to be tremendously beneficial for that anyway I would suggest, though a reasonable effect at least could be gained from it.
The best Yoga possibly for weight loss would be hot Yoga which I believe is done in steamy conditions, as that would make you sweat a lot more, which could have weight loss efffects relating to excess water weight.
It should be noted though that excess water weight can occur potentially from drinking too much water, but definitely from excessive Salt intake as can Hypertension in relation to excessive Salt.
Hot Yoga would therefore be benficial in reducing excess water and fluids in the body, through sweating, as long as the factor(s) causing the excessive water levels, got cut back to a level, where such an effect could no longer happen under normal biological circumstances, if that makes any sense.