How do I calculate the spring weight rating for my bike? I have a home built bike design and the rear shock absorber that came with the part bottoms out so I want to get one that is more appropriate. But I have no idea how to calculate which one to buy as far as the tension of the spring is concerned.

At Amazon for example there are many from 550lbs to 1500lbs shocks. I don't want an immovable spring nor do I want another weakling so how do I calculate what shock to get? 

ADDITIONAL INFO EDIT
I found this calculator
https://www.tftuned.com/spring-calculator 
I put in 210lbs - shock stroke 1.5" - wheel travel 4.5" - 33%sag

I don't have a clue how to read these results.
From that spring calculator site  "The spring rate is the amount of force required to compress the spring one inch, and is measured in pounds."

Your current spring is rated at 550 pounds according to the label

Optional - to test it, put the spring somewhere you can measure the compression accurately, and load it with 55 pounds of weight.  It should compress 1/10 of an inch and then rebound to the original length.  Likewise it should extend 1/10 of an inch if you hang 55 pounds off it.

As long as you're not exceeding its elastic limits then the spring will rebound to its empty size (so says Hooke's Law)  Otherwise it will permanently deform, but that will take a lot of weight.



Based on the numbers in your question the answers from the calculator are:

Single Pivot / DW-Link  


CCDB/5th(CVT)/Man(SPV)    764 lbs  
Fox/RS/Maz (shims)       859 lbs



This is a single pivot suspension: 


4 Bar / VPP 


CCDB/5th(CVT)/Man(SPV)    840 lbs
Fox/RS/Maz (shims)      935 lbs



This is a pivoiting suspension:



The other titles are brands


CCDB is probably Cane Creek
5th CVT is probably Progressive Suspension Fifth Element
SPV is Manitou air shock
Fox is Fox Suspension
RS is RS Suspension
Maz escapes me sorry
Shims is one way of adjusting the spring, by adding more washer-like obstacles to compress the spring sooner.


Given your bike is slightly non-standard, at the end of the day you're going to have to take a guess.  If your bike has a see-saw pivot in the suspension, go higher or if its a straight squash then go lighter spring rate.

You could also consider the normal load you exert on the saddle when it bottoms out.  Then imagine half that weight, and extrapolate from there.