Hi Brigitte and welcome to TE! Lovely name! (I have the same.)
I'd recommend you set achievable goals. Don't increase your mileage/time too much every week, many experts recommend 10% a week MAX, and only 3 out of 4 weeks (the fourth week you take it a bit easier because your body gets fitter when you're resting).
Don't keep your eyes on the scale, but pay attention to how you fit in your clothes and how you feel. Even put the scale away maybe.
Riding 3 times one hour a week is fine as you start. You burn the most calories when you're riding at a very comfortable pace, not when you're struggling, so find a comfort zone and stick to it. On one of your rides, you can push yourself a bit more in "intervals": go hard for a few minutes (or hit a hill) and then take it a bit easier.
The good thing about your heavy mountain bike is that it will make you work harder. The bad thing is that if it doesn't fit you well you could hurt yourself pretty badly and that that could impair your efforts to get fit. Be careful: if you feel pain, it's not just you, and you might need to make adjustments to your steed.
The most important thing for now is probably making sure you enjoy the rides. Of course you will still have to kick your b*** to get out of the door - we all do - but once you're there you should focus on having some fun. That's how you'll become addicted!!
Enjoy!