Whatever the reason that got you started in Pilates, or whatever your fitness level is at when you start, consistency is key. Improvements will take place with consistency. It is important to allow time for your body to recover in between your sessions to enable the body to make adaptations.
Learning Pilates is a progressive practice. It is likely that your Pilates workouts will involve you learning to move differently. This is particularly so if there is imbalance in your body from repeated movement patterns that work one side of your body more than the other in sports, or your job, or following injury, pain or a medical condition.
You should start feeling results from regular Pilates practice in as little as 3 weeks. You are likely to feel more energised, calmer and alert after your first few sessions, and you are likely to feel stronger, more flexible, and balanced after 6 weeks.