Frank has commented on issues with Charlson elsewhere (see links below, it sounds like you’ve already read these). There are certainly better options, and they tend to draw on the same data sources so there isn’t necessarily much overhead in applying a more modern variant.
To address your question specifically, inclusion of age as a weight component in the Charlson index score is going to be blunt. When we have worked in this space, we purposefully did not include age when developing those indices (edit for clarification: we did adjust for age when developing the condition-specific weightings for the indices, but it was not a weighted component of the index score), instead allowing analysts to separately include age as a separate predictor in the analytical models. This means that one can use these morbidity indices while allowing for better separate control of confounding by age – for example, accounting for age using restricted cubic splines in the modelling, as well as including your other (co)morbidity index using such splines.
I think that if one were constrained to use a (co)morbidity index that included age as a weighted component of a total score, then you could still include age as a separate adjustment variable. I don’t think there would be problematic collinearity, since the morbidity index will most likely be driven mostly by other components, and I would expect better adjustment for confounding by including age adjustment in a suitable functional form (again, because age as included in a weighted score would not be able to capture any nuanced relationship of age to outcome ). I’d be interested in hearing others thoughts on this.
A couple of links below on issues with Charlson for other readers: