Fitting a continous variable to another continous variable that is a component of the first continous variable I have an index that predicts orthodontic treatment difficulty based on several components each with a different weight (see the attached figure).

One of the components that is used in the index is patient's age, where the weight of the age increases as the patient's age increases. For example, a patient younger than 12 years is weighted 1.5 while patient more than 18 years is weighted 6.
The total score of this index ranges between 7.5 and 29.
Now I calculated the index score for 135 patients and wanted to perform a linear regression model of the index scores by the patients age. However, the patients' age is a component in the index.
Is this OK? If not, what should be the appropriate method to compare the index score to patient's age? Is it OK to divide the patients into young (group 1) and old (group 2)? Or perhaps only perform gender comparison?
Thank you

You're correct to be worried. Score will of course be correlated with age - it's a circular question. Probably your best bet would be to re-create scores without age - that would get at your question of interest. And certainly any analysis that does not use a variable that goes into the score, such as sex comparisons, is also fine.
