Advice on connecting heater directly to SP2 relay of PID controller?
I decided that I wanted to use the inbuilt SP2 relay in the PID controller. 


That's fine. 


  From the wattage of the heater, I know it would draw a maximum of only 1A and is going to be below that. 


That's fine too.


  The SP2 output from the PID has a small 5V energized relay with 3A load capacity. 


I didn't read the manual (but have used Omega controllers in the past) and don't know how you figured out that it uses a 5 V relay coil internally but it's not that unlikely.


  I would like to know if it is safe to use the heater directly with the SP2 relay terminals of should I use the SP2 relay to run another AC relay for the heater?




Figure 1. Waveform for short-period duty cycles from an SSR. Source: LEDnique.com.

You can do either. For relay operation it would be normal to set the output duty cycle period to 5 s minimum. This is to reduce relay and contact wear. If your heater's thermal response is too fast and you require a shorter time then you should use the SSd output which will provide a 5 V signal for an SSR. This you can switch much more often - even down to 0.5 s but be aware that your SSR will, most likely, use zero-cross switching and that with very short periodic times you will be switching on for only a few mains cycles.