I don't have any experience with the Honda CR-V, I too having just bought one last week 2015 Honda CR-V EX AWD, fully loaded with all the goodies). That said, I do know about windshield washer systems, from back in the days when I owned a 1963 VW Bug in 1969. These washer systems all work the same way.
Front: There's an electric pump that pumps water from the windshield washer tank (usually in the engine compartment), through hoses and out the nozzle(s) at the base of the front windshield. Your system has two nozzles, one for the left half of the windshield, one for the right side. Some cars have one nozzle that sprays water in the middle of the windshield, which is then spread by both wipers.
Rear: That system works independently from the front unit. It has its own pump, hose, and nozzle.
Note: The pumps are NOT all that powerful. End result, it does not take that much to interfere with the flow of water out the nozzle(s). Moreover, keep in mind the pump is designed to gently spray or drizzle fluid/water, this so that you do not spray fluid on to cars behind or next to you on the road. (Think road rage!)
BEFORE DOING ANYTHING, CHECK THE WINDSHIELD WASHER FLUID TANK. Sometimes the problem is that there's no fluid in the tank! Just as people whose car stops running simply ran out of gas, so too do they let the washer system run dry.
The Nozzle(s): Since you are getting some water flow, and if you're not simply running on an empty tank, my money is on the nozzle(s) being clogged. E.g., many people polishing their cars get wax or other products on to or in to the nozzle hole. The wax dries out, boom, a clogged hole, the stream slows to a trickle.
How to fix: First get the tools needed for these various fixes. A can of compressed air, a flashlight, rubber bands, a turkey baster, paper towels, and a magnifying glass.
With a flashlight and magnifying glass inspect the nozzle(s) closely. Accumulated wax is usually a dingy white or yellow color. The accumulation will be the size of a pinhead. Also, look to see if there's something else clogging the nozzles. All kinds of things can be clogging the flow, either at the nozzle(s), in the hose, or the fluid washer tank (at the bottom). Make sure the wiper area does not have leaves or other debris in the windshield sill. (Sometimes the nozzles can be clogged with dirt, dust, sand from the beach, or even towel lint from the car wash).
If you see a nozzle has a blockage, carefully, with a gentle touch, move the safety pin in a small circular motion to loosen the debris. DO NOT PUSH THE PIN INTO THE NOZZLE HOLE! You risk damaging the nozzle. After the debris is loosened use the canned air to blow it AWAY and OUTWARD from the nozzle opening. Don't blow it further into the nozzle.
Test the washer, see if it now works you're in business. If that didn't fix it, I would next check the windshield washer tank. (Again, is the system simply out of fluid or water!!).
The Fluid Tank: Use the turkey baster to empty the tank. (Yeah, if there's a lot of fluid in the tank this will take some time. If you have a pump or hose you can try siphoning/pumping the fluid into a plastic jug or bucket, so you can reuse the fluid, and draining will be faster.) Warning: some washer fluids may be toxic, so don't use your mouth to siphon the fluid. YOU MAY OR WILL DIE, or at the minimum look like a moron on the nightly news broadcasting "Man almost dies when he stupidly swallows windshield antifreeze washer fluid Said he was trying to fix his Honda windshield washer system. A Honda rep commenting on the CR-V owner called him a moron."
After the tank is empty take the flashlight and inspect inside the tank. If people use plain ol water in the tank, the water may have been dirty, thereby clogging the hole or opening to which the pump is connected. The tank may have a filter to catch the debris inside the tank.
How to fix: This is simple. First: INSPECT THE TANK. Is it cracked, to where it will NOT hold fluid? Those plastic tanks do fail, look for cracks on the side or at the base. If it is damaged get a new tank on eBay or elsewhere and replace it. If it is not in a difficult spot to reach you can fix it yourself. Or have a trusted garage take care of it. That's a small job to do. $50 including the price of the new tank.
- If there's grease, sand, dirt or debris inside the tank, clean it out. Rubber band paper towels to the end of a screwdriver, move it around inside the tank to soak up debris. Repeat the process with new towels as the old ones become dirty, wipe the walls of the tank until it is clean of all debris. Use the flashlight to inspect your work.
Note: It helps if you have two people when testing the system's functionality. E.g., when pressing the switch inside the car, you can look inside the tank to see what's happening. Same thing for seeing what is happening at the nozzle(s).
Other Things To Check: There may be an air bubble in the system's tubes/hose(s). Run the system with water until the bubble dissipates and flow is back to normal.
Check the hoses/tubing to the extent you can. Your CR-V is not old enough for the tubing to develop cracks. But someone may have damaged the hoses/tubes when working on the engine or in the compartment. If your lucky the tube(s) run from the tank to the nozzles to where you can do a visual inspection. (I just bought my 2015 CR-V so I don't know anything about the engine compartment. But I did notice that there's LOTS of room inside the compartment, making access to most anything quite easy.)
Also check to see if the tubing is fully connected to the various fittings, such as at the bottom of the fluid tank. A tube may have come loose resulting in a slow flow, similar to your house vacuum hose not being fully seated.
- Disregard the comment that this must be a flood car. That member was probably joking, but if he's not, that was a mean and silly thing to say. He was probably lashing out in envy at your getting a good deal on a car that is basically new.
- The good news for you, since it is pumping water that means it is NOT the motor (pump) which can be expensive to replace.
- Don't ever take your car to the dealer for service or repairs. IMO they are rip-offs. The dealer owner's goal is to make as much money as possible with as little effort or work. E.g. is your problem. It is far more profitable to replace the entire washer system than to diagnose the problem and fix the issue. Go on your local Yelp and search "mechanic Honda" or "car repairs Honda" - find yourself a local independent Honda specialist WHO HAS FOUR OR FIVE STARS on Yelp. Also make sure the garage has lots of reviews, not five or six (half if not all those reviews the garage's family posting phony reviews).
If you want to DIY (do it yourself), go on YouTube to see the many videos people post on how to check and/or fix a windshield washer system.
Bottom Line: Your car is too new to have major problems that develop from old age. Rotting hoses, cracked tubes, broken nozzles, filthy fluid tanks, that's stuff that happens when a car ages ten years or more. If you're not mechanically inclined, fixing your washer system is a great project to make your mechanic DIY bones. Otherwise, take it to a highly rated local independent garage to fix the problem. He or she will charge you $30 to $50 to fix this. $100 to $150 depending on what parts are needed.
