B737-800 First Officer reported a FLT CONT EICAS light illuminated in cruise. The Flight Crew returned to the departure airport and reported that during landing the flight controls felt sluggish and the aircraft had a yawing motion.

Narrative

While cruising at FL350 along Airway X between ZZZZZ and ZZZZZ1 intersections; the Master Caution light illuminated along with the FLT CONT system annunciator light. After saying 'Your Aircraft' to the Captain who was Pilot Flying for this leg and the Captain responding with 'MY AIRCRAFT;' we looked up to the overhead panel and saw the LOW PRESSURE amber light illuminated to the FLT CONTROL B side. I opened the electronic QRH to page X and read the following Condition: 'Hydraulic system pressure to the ailerons. elevators and rudder is low.' After also reading the Objective; we accomplished the only step in the QRH by moving the FLT CONTROL switch on the affected side; after confirmation; to STBY RUD. This action illuminated two other amber lights: YAW DAMPER and FEEL DIFF PRESS. There was no mention in the QRH that these two lights would subsequently light after moving the FLT CONTROL B switch to STBY RUD. After seeing these two additional amber lights; I opened the QRH to review the instructions associated with these 2 amber lights. The FEEL DIFF PRESS QRH step said to continue normal operation but that control column forces may be higher than normal; particularly during the flare. We discussed this as a crew. We then reviewed the YAW DAMPER light QRH steps; followed them and reviewed those instructions as a crew (including not to land with flaps greater than 30 and to avoid moderate or severe turbulence). The YAW DAMPER amber light remained lit after following the QRH steps. After briefly discussing the option to land in ZZZ; the Captain made the decision to return to ZZZ1. I informed ATC of our desire to do a 180 degree turn and return to ZZZ1. The ATC Controller asked why; and I responded; due to a flight control problem. The Controller gave us instructions to turn north and then gave us a clearance to return to ZZZ1. The Controller also asked if we needed further assistance; and I stated not at this time. During the turn back to ZZZ1; it was obvious the YAW DAMPER system was not working as it felt like we would slip and slide through the air in response to every gust of wind. This was even more pronounced on final approach. En route to ZZZ1 we reviewed possible diversion options should we lose hydraulic quantity or pressure but both remained stable; although System A side QTY had reduced to about 80% from 105% at departure. En route; we lowered our altitude to increase fuel burn and reduce fuel on board as much as possible. The APU was also started for that reason. We read the FOM requirements for an overweight landing which clearly state that [priority handling must be requested]. As we checked in with ZZZ1 approach; I [requested priority handling] and our intentions to conduct an overweight landing with a flight control problem in ZZZ1. I asked for Runway XX with no LAHSO (Landing And Hold Short Operations) restriction. The ATC Controller asked for other information like fuel on board in minutes and souls on board. We had XXX souls on board. During final approach the Captain stated the flight controls felt sluggish and I could feel the aircraft slip and slide in the YAW axis. The Captain made a smooth landing at a low vertical rate of descent and we exited the runway and taxied to the gate with no further incident. CFR had been called and they were there along side the runway if needed. Possible blockage in the B side Flight Control Hydraulic lines.No suggestion on how to prevent this; but I would suggest adding additional information to the FLIGHT CONTROL LOW PRESSURE section of the QRH that includes the possibility that the YAW DAMPER and FEEL DIFF PRESS lights could also illuminate and to follow those QRH steps and discuss those flight implications as a crew. The QRH implicitly treats this flight condition as very benign due to the simplicity and lack of info in the QRH for this flight problem. Is a potential blockage in the hydraulic lines to the primary flight controls really a benign condition? A context to the severity or non-severity of this flight condition would be appreciated so that decisions on continuing flight or diverting can be better made.