무겁다 means "heavy" 묵직하다 means "heavier-than-expected"

Hello. :) I'm a native Korean. 1. 묵직하다. When I lift something which is not shown (for example, it's placed in the bag), I guess something in the bag is heavy. In this case, I say '묵직하다.' 2. 무겁다. Regardless something is shown or not, if I feel it heavy, I say '무겁다'. '무겁다' is more generally used than '묵직하다'. Hope it helps :)