Tennis leads to muscle imbalances.
Your "hitting muscles" get stronger and stronger from all that ball bashing.
Your whole dominant side gets stronger and stronger - pulling your back out of alignment.
To play as much as you do, you need an off court program to continue to play and not be plagued by a series of overuse injuries.
(And yes, you need more rest now, and to build more rest into your program.)
Here is a minimal off court program that should help:
Thrower's Ten Exercises: http://www.muhlenberg.edu/pdf/main/a...throwers10.pdf
Tennis Weight Training - Exercises of Weight Training for Tennis http://optimumtennis.net/tennis-weight-training.htm
Tennis Elbow: Step-By-Step Instructions For Treating Elbow Pain Using A Flexbar (Tyler Twist) http://www.youtube.com/watch?v=A2QQaVfeI4U
You mention you used to do fairly heavy weight training.
To prevent overuse injuries you don't have to "lift heavy". Even fairly minor increases in strength - especially in your non-hitting/non-dominant side muscles - can help prevent overuse injuries.
(Of course if you have the time, or have an offseason, getting even stronger can help build up more of a reserve for the long tennis season.)
Here's a good source if you want a balanced training program that will take more time:
Sports Fitness Advisor Tennis Training Section: http://www.sport-fitness-advisor.com...-training.html