Running power changes when weight changes?

See this Garmin support document

https://www.garmin.com/en-US/garmin-technology/running-science/running-dynamics/running-power/

Also if your prior was using the HRM , that could be a factor if the HRM was a HRM with Running dynamics as although those may be similar to the watch , they are not identical.

I would also think if you are lighter you apply less power at a specific pace - thats a lay person thought.

Newton's laws apply. Using dimensional analysis:

1 watt = 1 joule/second = 1 newton metre/second = 1 kilogram (metre/second²) (metre/second) = mass × acceleration × distance ÷ time

The power needed to move a body in the same manner increases in direct proportion to its mass.

However the ratio of 392/46.21 (8.5) is greater than 311/45.32 (6.9), so, yes you may have got a bit weaker according to the numbers

The only other factor is using a HRM strap versus the watch's optical sensor. That would definitely affect the calculations.

Just to clarify, are you saying I need to use my HRM pro in conjunction with my 955 for a more accurate reading? 

Understood, but the discrepancy is too large. I am running faster times with 70 watts or more less. The only difference is that I don't have my HRM pro at the moment and running without it. 

My point is that the figures from a HRM-PRO and the watch are not exactly the same. Look at any of the RD metrics you recorded with the HRM-PRO and with the watch alone and they are slightly different (well they are in my case) so that may have an impact.

To me all these figures are about trends with the same device , not absolutes.

You need to use the same combination of sensors to ensure consistency.

Thanks all. My understanding was slightly different, I understood it from cycling terms and FTP. Power stays the same regardless of how much you weigh. If you pushing 300w, it should be 300w irrespective of how much you weigh. A friend of mine suggested the same thing and said I need to continue using my HRM pro which again will give you a higher figure. I just don't understand the differences as I thought it would be the same, as with HRM Pro my rFTP is 450, and without its 390. 

Looking at the Garmin document:

 https://www.garmin.com/en-US/garmin-technology/running-science/running-dynamics/running-power/

Have you looked at the stride length,  cadence and other ratios in both activities that are similar speed and distance , with and without the HRM . There is a difference in them from watch and HRM (in my case anyway)  , likely given the placement and stability of the HRM vs the watch.

I would say that my HRM Pro is more precise than the one on the watch - and as a result the FTP will be different.