So if I change from 125 gr broadheads to 165 gr broadheads will this change the spine of my arrow?

yes, it will make it weaker.

It will weaken the spine - that is for sure !

So how does one add weight to the arrow without changing the spine or can it not be done?

You could try 3 gpi weight tubes if shooting carbon arrows,these will have little effect on spine.But they will pop your nocks out on a hard hit.Or if your arrows are long enough you could try cutting the length alittle.

Here are my specs; cedar arrows 26.75 inches long 65 to 70 spine 25.250 draw lenght 54# recurve. Shooting very well with what I have just thought more weight hits harder and gets better penetration. I am using this for deer this year but want to go for elk next fall. Also the arrows weigh in at 525 was thinking I would like to get them up around 600

If you cut your arrows 2/3 -3/4" you should be OK to compensate for increasing tip weight from 125 to 165.

you could add a footing, internal or external, that would stiffen the front end and allow you to use a heavier head.

Just cut 1/2" off of the shaft.40gr won't make a big difference anyway.

I don't think anything is wrong with what you have. Your use to how they shoot, windage and elevation.

May wish to consider bare shafting some 175 gn field pts to provide you some perspective.

I say stick them on and see how they do. Might not have much effect on them at all. If they do, like said above, cut some off.

Try them first. If they're a little weak, you can build out the side plate by a sixteenth or so. I did that myself with the set I made for hunting this year. You can also add a heavy set of string silencers to absorb a little of the excess energy. You may be able to get good flight without having to trim your shafts.