Potatoes are actually super filling per calorie, one of the first and best foods I recommend for weight loss. The potatoes/eggs/cheese combo is especially filling, basically you’ve dialed into a budget conscious survival meal.

But you need to gain weight without spending much more money. What do you have to cook with? Knife cutting board pots pans stove?

First great option is soup. Pre fry aromatics directly in the pot (carrots, celery, onion, whatever you can get). Be HEAVY with oil, I recommend light olive oil. Heavier than you probably think with salt too. Then add mass (potatoes) and water. Dried lentils and split peas don’t need to be soaked overnight, just add them in and let them simmer for the last half hour. Tons of cheap calories and seasoning. Season with anything you have.

Then get into white rice. There’s a cost barrier here but if you can save up enough for a large 20lb bags the cost per meal is extraordinarily low. Tons of calories and doesn’t really fill you. Have it with the soup or as a bed under other veggies. Overdoing it with the rice can cause some health issues relating to blood sugar but it’s an extremely easy and cheap way to add 2-400 calories to a couple meals a day.

Check clearance for oily sauces. This is basically the reverse advice compared to weight loss - a lot of innocuously small jars can easily contain over 2,000 calories. If you can get them at 25% cost that’s a ton of weight gain potential and will help give you flavor variety and make your meals more calorific.

Just a few thoughts. Wish I could help, I know this situation sucks