C185 pilot reported a NMAC in deteriorating VFR weather conditions when they descended in front of another aircraft on the same heading.

Narrative

I and a copilot were returning from a supply drop at ZZZ1; as part of relief efforts. We were en route back to ZZZ. The weather began deteriorating and ATC was too busy to help with all VFR flight following requests. Because of developing cloud formations; we had to find a hole to get below the cloud layer in order to proceed on course. It seems that the other Aircraft found the same hole and was also in route to a local airport as part of the relief effort.We were initially higher than the other aircraft and presumed that the aircraft would remain on course and pass below us. However; the other aircraft turned to the their right; joining our heading. As such when we arrived at their altitude we were approximately 400ft behind them (we have confirmed this by studying the historical ADS-B data). We have no reason to believe that the other aircraft saw us.We promptly turned and no further action was necessary.We should not have presumed that the other aircraft would remain on a straight course after our initial sighting. Additionally; we should have preemptively ceded right of way as the other aircraft was below us.We usually request flight following; which would have aided in this situation; but the but we were not able to get flight following for a few more miles because of ATC workload. The relief efforts stressed the ATC system (they were doing great; all things considered!).Additionally; the degrading weather meant that VFR aircraft had fewer options for navigation; further contesting the VMC airspace.