I left my first job after around 2 years and joined a competitor .. Salary increment was not too much (less than 5%) but it is much more stable and bonus greater .. After including bonus, annual compensation is 35% more than previous job... And it is much safer while the previous place was always retrenching ... Sometimes it's not the salary but rather the annual compensation..

They asked for the hardcopy, looks like they are not calling the referrals.
I don't have have hardcopy, as I thought usual practice is to call? So am wondering if it's OK to ask them to call instead?
Also, does it matter if referral is supervisor or co worker?

Tell them that you do not have letters from your referees, but they can call them to check on your work performance and attitude if needed.

Usually the only referees that have any influence at all will be your managers. Remember to check in with those people to give them a heads-up that they might get a call from whichever company... and of course to help paint u in a good light.