Quite interesting question. While there are two forms 重い / 重たい, 軽い, which is the anatomy of 重い, has only one form and there's no 軽たい. I looked it up on google then found it popular for Japanese learners. Here is the article which helps you make it out. http://jp.hjenglish.com/new/p422914/

There are not many pairs of adjectives that have -たい and -い forms. Actually, I only found 煙い/煙たい（けむい/けむたい: smoky）. When the smoke is 煙たい, it bothers you more than when it's 煙い,I think.

それは重い＝It is heavy. それは重たい＝I feel it heavy. so 重い is just same as heavy. 重たい　is not indicate a fact but feeling. 重たい＝私はそれを重いと感じます 眠い and 眠たい are almost same, pretty close but I think 眠たい　is more sleepy than 眠い someone might not feel so.