Why do I feel melancholic so much?

We humans are social beings and need loving interactions, especially when we are young. As children it is also important to have secure attachments to our parent or caregivers. Your question does not make it clear why you were often left alone, nonetheless, the result was that you felt lonely. Your memories are vague. Many times children do not have vocabulary to express themselves, the memories can be sensory, or body sensations. It could very well be that your senses are triggered if you are in a stuffy room and the sighing could have been your attempt to self-sooth because a sigh mimics deep-breathing, which is helpful comforting your body, which sends a message to the mind that everything is okay. 

Very often pathology begins in childhood and we carry the ideas of not being loved or unworthy because the adults in our lives were not around to provide the nurturing required of a young child. This can sometimes lead the child to believe that he/she did something "bad" and result in a negative self-concept. These childhood memories of being alone were maladaptively stored and have stayed with you into your adult life. You learned to combat the melancholy feeling by keeping busy. When you are not busy, the childhood feelings return. You regress to old behaviors of sadness and mend it by keeping busy.  The key to conquering the melancholy feelings, is to lean into the sadness, feel it, learn from it and find language to discuss it. If you can name the emotion it will lead to clues that will unravel the mystery of why melancholy takes over when you are idle or have free time.

Healing will take form in cognitive restructuring of self-talk and being kind to the young child within. As an adult you can tell that child you will protect him/her and teach the child to get attention in a positive manner, which includes living a balanced life of work, quality time with friends and relatives, self-care of good nutrition and getting sufficient.. And last but not least, forgiving those who neglected to see you, hear you and love you.