Should I submit one strong recommendation letter or one strong letter and one weaker letter?
It depends a lot on how you define "a weak LoR". Consider 5 levels:


+2: My best student in 10 years.
+1: DWIC (did well in class) + hard working, take initiative etc
0 : Simply DWIC, e.g. Kerkyra's LoR.
-1: He was in my class, he asked me to write LoR.
-2: Don't take him


Unless you make someone very upset, people will not write a -1 and -2 LoRs. If you believe the weak ones are still +1s, you can submit.

FYI, I fell out with my Master thesis advisor, and decided not to use his LoR (he still offered to write one). I managed to get 3 PhD admissions with full scholarship using three +1 LoRs (but I submitted more than 50 applications).

Good luck!