@nickale Stress can impact how well your body deals with hormones, increasing cortisol it stress hormone can mess with the hormones your body uses to store and break down energy.
You could theoretically be eating the same diet as an identical copy of yourself and if the other one is not stressed they would lose weight.
In terms of bodyweight exercises do what you can. There is an element if trying it out to see what happens so keep it simple.
Squat, hinge, push, pull are the fundamental movements but If you dont have equipment either modify or leave it now until you get equipment or get stronger.
I would probably start with squat, pushup and plank. 3 sets of 5 repetitions to find your base. Rest a minute or 2 between sets.
You might be able to do more, might be less but you want to find your starting place so for the first week understand where your limits are, so that you know what you need to do to get stronger.
3 sets of 5 squats might be easy, might be hard. Do it and see, next time change it or keep it the same if it was just out of reach.
Pushups, wall, counter, stair or on floor but on you knees, again see what you can manage. Aim for 3x5 on the counter but can only do 2? Go back to wall pushups, might need to increase to 5 sets of 10 then go back to counter?
Plank, start with 3x5 seconds. Again Could be knee plank or just press up position. Add 5 seconds next time so its 3 sets of 10 until you csnt do it. That's your starting place.
Good luck!