I like to fast on Fridays (1 meal that day only), it's something small I can offer up each week. However I am also underweight for my height. I am not the type of person to each much, frankly overweight people underestimate how much they eat while underweight people overestimate how much they eat, so in order to gain weight I need to calorie count, otherwise I simply won't be eating enough. Let's say I need ~3k calories a day to gain weight, and eat ~1k each meal. Eating 1 meal on Friday means I will be in a calorie deficit for the week. If I were to increase my calories on the non-fasting days would this go against the Spirit of Fasting (as I am making up for the 'lost' calories)?

I am a male btw. Also if I wanted to 'bulk up' I would need to eat ~3.5-4k calories a day, would increasing my regular meals to ~1.5k calories also go against the fast?

You have to take care of your health.  If you need to gain weight, fasting might not be the best penance for you.  Seek out a traditional confessor and describe what you've described here, and do what he tells you.

In any case, fasting refers more to the quantity of food eaten, rather than the calorie count.  The latter is a question of prudence.  In theory, you could fast by eating small amounts of high-calorie foods.  There are also dietary supplements and nutrition drinks of which you could avail yourself.

Fasting shouldn't feel good. I'd call it fasting if you went all day without eating, and ate 1.5k at 7pm. Do you really need more fat? I don't know what is ideal in that regard, but I don't think your health will suffer if you stay skinny and light. Light is good for your joints, and it helps gives you a high power to weight ratio. You can add muscle weight instead of fat, just exercise with greater intensity, and eat a lot of protein. I'd watch out for eating a lot more increasing lust. Many saints practically starved themselves. Getting to heaven is what really matters, just as long as you are healthy enough to do God's will. Wait until you are 30-40 and gaining weight becomes easier for most people.