I think weight loss and building fitness are hard to do at the same time. Not impossible by any stretch but hard. If I want to raise my FTP I need to be well fed so that I can optimize my workout performance and “raise the bar” week by week. If I want to lose weight/fat, I have to have a caloric deficit so that I can burn more calories than I take in.
The two are naturally conflicting which then makes it hard to do both well simultaneously. I would say it’s impossible to “optimize” fat loss and FTP gains at the same time. You can lose fat and build FTP, but each will improve at a slower pace than if the entirety of the focus was on just one aspect.
I was able to go from 190lbs (untrained) to 170lbs over about a 3 month period. This was a drop of between 1-2 lbs per week. I’ve been stable at 170 for 3 months now as my focus has shifted to increasing my FTP.
How did I do it? The honest answer is you don’t need to workout at all to lose weight. In fact, the harder I train the harder it is for me to lose weight. So rather than fighting against my own goals, I made the determination to lose weight as my number one priority. I did very short bike sessions (30-45 mins tops) and generally didn’t care how many of those I did or didn’t do every week but averaged only 2-3 hours on the bike weekly. I would do a HIIT style workout, generally riding outside or on Zwift for a lap of whatever the course of the day happened to be and then I would get off the bike. Enough to maintain some fitness or even improve slightly but not enough to build a dramatic calorie deficit that would make me want to eat, and eat again and then eat some more. The more I would ride and especially the harder I would go, the more I would have the unrelenting feeling of being hungry. If I could keep it to short but hard workouts, they were easy to refuel and I could run a 500 calorie deficit (or more at times) and the weight just fell off.
So my short answer… decide what is most important; weight loss as a priority, FTP gains as a priority or time. By time I mean if you aren’t in a hurry you can do both, lose weight and gain FTP, but it will take longer to reach your goal with each.