Lessons I've learned over 30+ years of working.
1) Leaving your job for another one is the fastest way to increase your pay.
Companies have fixed “merit” increase schedules that don't account for inflation. They almost never take into account current market rates either, so the longer you stay with a company, the more you lag behind the current market price for your skills.
This starts to become slightly less true as you reach the top salary tier in your area, but early on, you should be looking to learn as much as you can and move around to get the best compensation for your skills.
2) You don't owe your company 2 weeks notice when quitting.
I have both given notice and walked off jobs with none, depends on what they did and my reasons for leaving. If I need a recommendation or something else from them they get a notice, if they are terrible and toxic, buh bye.
3) HR isn't there to protect you, they are there to protect the company from you.
4) Salary isn't everything.
The highest salary per year isn't always the best value, look at what else that company brings to the table. The total cost or value of the benefits plus a lower salary may be a better deal than a higher salary with few or no real benefits.
5) Once you decide to leave…leave.
If you get a counter-offer never accept it, that counter-offer buys the company time to replace you. It really doesn't benefit you at all.
All the begging, pleading and playing on your sympathies won't change the facts as they are, something drove you to want to leave and it is unlikely to change if you stay.