This is the 282nd most frequent Arabic word.
بحق
Rightfully; truly; deservedly.
Here 'بحق' is used to express the sincerity and intensity of the trust.
أنا أثق بك بحق.
I truly trust you.
Here, 'بحق' is applied to indicate that the accomplishment deserves recognition justly.
هذا الإنجاز مستحق بحقه.
This accomplishment is deserved legitimately.
In this sentence, 'بحق' indicates fairness or justness in the context of the speech made.