The type and weight of the oil will have no effect on how hard it is to actuate the clutch.
The pull is affected by the condition of the cable, the condition of the actuator arm, and the rate of the clutch springs. The springs will have the greatest effect.
Now, here's a twist. You have a 2011. Kawasaki changed the clutch in the middle of that model year, so we need to know your engine number in order to know what clutch you have and what someone may have done to it. What we need to know about your engine number is whether or not it is above or below KL650AEA72319. You'd find the engine number stamped on the right side case as shown in this post: https://www.klrforum.com/35186-post2.html
I'm not too smart yet, and may never be, about the later clutches. I do know what sorts of springs can be and have been put in the earlier, before KL650AEA72319, ones. As you mention, the KZ springs are popular. So are Barnett. The Barnett's will run about 50% more force than an OEM spring.
The later, after KL650AEA72319, springs have a lower spring rate but they are really long and have the same installed height as the earlier ones so, generally, they are about the same stiffness as the earlier ones. I haven't seen the Barnetts for the later clutches yet.
Get your engine number so we can talk smart and figure out what might be in there.
Meanwhile, remove your cable and check that it is very easy to move the cable. Once that cable wears through the liner it can get rather hard to move when it is under tension. There's fairly high friction between the cable and the housing coil once the liner is worn through. Also, look for a bend in the cable at the clutch lever. If it has one, then the PO put a Gen 1 cable on. That could be a problem, too. I think they are a bit shorter. The things are about $15; replace it if there is any doubt.
While the cable is off you need to make sure that the arm moves freely. I've never seen one that was frozen, but there is a bearing at the top. If that has gotten rusty or somesuch that could be a part of the problem.
If it comes down to the stiff clutch being due to heavy springs there are three things you can do. 1) make your hand stronger 2) replace the springs with OEM 3) get Twin Headlight Ernie's extended actuator arm.
Here's an article with a whole bunch of shit about KLR clutches and an article about Ernie's actuator: