Best way to say something affects another but only moderately?

There is a saying that "Correlation does not imply causation." I am trying to find the best way, preferrably in a word or short phrase, to explain when one thing really does have a causal effect on another, but the effect may not be strong.

This might be more clear with examples. People tend to get better with experience, so years of experience really might cause someone to be more skilled. But there are so many other factors (intensity of that experience, amount of study and practice, etc.) that the effect of experience might easily get swamped out and someone with fewer years of experience might be more skilled.

Similarly, exercise can help cause weight loss. But diet and genetics often play a bigger role than amount of exercise in determining how much someone will weigh.

One phrase that I think comes close to my meaning is "loosely coupled", but I don't think that quite captures it and for people with a software development background it will carry a very specific meaning. So what is the best way to express this?

I think you're looking for "influence". As in:

Certainly diet and exercise influence weight regulation, but genetics and ingrained eating habits predispose many of us to gain weight.

Alternatives for predispose include bias, sway, and skew, all of which mean to incline (ie make more liable) something towards a specific condition, without totally determining the outcome.

Related (“Standing in relation or connection”), linked (“connected, either with links, or as if with links”), and connected all are possibilities. (Note that related, like correlated, does not imply causation; and to some extent the same criticism applies to linked and connected. For specificity, perhaps say causally related, linked, or connected.)

My go-to way to categorize such impacts is by stating that the additional source as having a secondary or tertiary impact.