Yes, bodyweight training can help you build muscle. But that does mean it will make you heavier.
Your weight is a product of energy balance (calories in v calories out)
If you consistently consume fewer calories than you burn you will lose weight, regardless of whether you are resistance training or not.
Where bodyweight strength training (or any other form of resistance exercise) becomes really important is dictating where the weight is lost from. Fat stores or muscle stores. Regular resistance training will send a signal to your body to preserve/build your muscles meaning the only place left to lose weight from is your fat stores. This is the ideal scenario for weight loss.
A simple formula you can use to remember this:
Sustainable Calorie Deficit + Progressive Resistance Training = Effective Weight Loss
Bottom line… if you are not losing weight you have a calorie issue, not a strength training issue!
PS - For those who want to gain weight the same principle holds true. Bodyweight strength training by itself won’t make you heavier. You will also need to ramp up your calorie intake until the scale weight starts creeping upwards. Regular resistance workouts will then ensure plenty of these extra calories get diverted to building muscle as opposed to simply being stored as fat.