What are the ways to increase device Screen On Time? I have a device with 2500 mAh battery and I usually get around 3hrs+ Screen On Time. Are there ways to gain some more juice...? 
[I am a rooted user, so any method (root/non-root) are welcomed.]
The Screen On Time (SOT) depends on lots of factors like the way you use your phone, apps that you have installed, the strength of the mobile signal in your area, the data service that you have (2G, 3G, WiFi, LTE).

So it's hard to suggest anything specific.

What you can do is- use any battery statistics app (Like Better Battery Stats or Wakelock detector) and find out the apps/ services that are draining the battery. Then you can restrict these apps/ services based on your needs.