15lb V 14lb that is only a 7% difference in weight. Yes may help with reducing stress on the elbow/arm.
But the route cause needs to be looked at.
Have you been to a coach who would look at your swing/timing to see if that is a  cause of the problem..?

I am pretty sure i have tennis elbow. I also forgot to tell you that I just turned 60. So i guess 50 years of bowling finally caught up with me.

Being that you just turned 60; when was the last time you had your grip checked?  If it has been awhile; as you already know you are going to lose some flexibility in your hand.  So it may be wise to have your span and pitches checked.  I know everyone is built different, but as a reference, I am about to turn 52 and bowled for over 40 years and pretty pain free.  I am sure by the time I reach 60 some things will change for me as well.  But it is always a good idea to make more frequent visits to the pro shop just to make sure things are where they need to be.  What you could do in the meantime, is go to your pro shop and grab some undrilled balls of various weights until you find one that doesnt bother the elbow so much before deciding to put holes in one (or more). 

So if you make this change in weight is it a big difference? How much of your  ball reaction is affected? Also how long will it take to get comfortable with the change? Does it affect your PAP and layout?  Will it help with elbow pain? Or at least reduce the pain? I am contemplating if I need to make the switch?

I have friends who made the switch like you're considering, and some went back to #15, some stayed at #14. The lighter weight doesn't create as much messenger/sidewall action IMHO.

If it's tendonitis, dropping down in weight is just a temporary band aid. The only real cure for it is rest.

Keep rolling a heavier ball as long as you can, and like other posters wrote, check your grip and arm swing. Good luck.