Giving significance to something is important, and there are many synonyms that can be used instead of "according due significance to". These synonyms include "emphasizing", "highlighting", "focusing on", "prioritizing", "placing importance on", "valuing", "placing emphasis on", "acknowledging the importance of", "recognizing the value of", "paying attention to", "taking into account", "esteeming", "treating as significant", "regarding as important", "appreciating", and "considering seriously". All of these words indicate the importance of assigning meaning and weight to a particular concept, idea or object. When you use any of these synonyms, you can convey the importance and relevance of something effectively.