What's important is to make sure to focus on cardio more then using weights. You'll see results faster this way. Your doing wonderful! 3 weeks you should see inches coming off for sure! You'll probably notice baggy pants before anything else! Good for you!
It sounds like you're already noticing a difference. I would pay attention to how my clothes fit...when I start needing to pull my belt tighter I'd know I was seeing results!
a month is probably a good amount of time to start seeing some small changes. Keep in mind to not go by what a scale says since you will probably be adding muscle. Go by hopw your clothes fit