You’ve got a long way to go if you want to do endurance competitions if your horse is overweight and you’re only riding 2x/week. I conditioned one for 25 mile rides. He was not overweight and reasonably fit when I started. Then, I slowly worked up to longer and faster rides. I have never ridden a Paso Fino before.

For getting him in shape in general, just slowly increase the time and intensity of his workouts. The key word is slowly.

You want to build stamina. Find a hill with a gentle grade, not too steep, and do trot sets. Trot for 5 minuets. Take a walk break, then do another set. You can increase in the length of the sets and the number of sets over weeks. Move up to steeper hills as you progress. This builds stamina and muscle.

Just slowly increasing exercise is the best way to go. Start with brief rides on flats, slowly increase inclines, number of times a week, speed, and distances ridden. Your horse will let you know if you’ve done too much too fast. As his activity level increases, you may need to revise his feeding, so keep an eye on his weight and adjust accordingly. Lunging your horse on the days you don’t ride will also help a bit with getting him in shape.

To start on endurance i would at first try to trot for long distances then trot and canter.