I can’t speak to how the letters are weighted, but I applied to UNB this cycle without LORs and was accepted. Stats were not exceptional, 156 lsat, 3.83/4.3 GPA (B3, self-calculated).
Because UNB specifically states that LORs are not required, I don’t think you will hurt your chances by not submitting LORs. On the other hand, a really good LOR that speaks to your character and ability as a student could definitely help your application—to what extent I’m not sure. Clearly, in my experience, LORs are not the be-all and end-all of an application.
Best of luck!