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The phrase "a weaker influence on" is correct and usable in written English.
It can be used when discussing the impact or effect that something has, particularly in a comparative context.
Example: "The new policy has a weaker influence on employee productivity than the previous one."
Alternatives: "a lesser impact on" or "a diminished effect on".
Exact(8)
The increased distance to Health Board headquarters in more peripheral areas may lead to a weaker influence on governance, one of the contingent elements described by Copus [ 7].
Concentration polarization is shown to have a weaker influence on the full-scale RO process performance than the thermodynamic restriction.
On the contrary, lagged negative returns have a weaker influence on cash outflows from SR funds compared to the conventional counterpart.
The background energy level which is determined by the backscatter efficiency and the lattice symmetry is shown to have a weaker influence on the maximum fill ratio.
Propionic acid degradation is largely inhibited during periods of high activity of the butyric acid-converting bacteria, whereas acetic acid exerts a weaker influence on the conversion of propionic acid [59].
In left middle temporal gyrus, there was lower activation for targets in O+P+ than all other lexical conditions, suggesting that converging orthographic and phonological information resulted in a weaker influence on semantic representations.
Similar(52)
We hypothesized a weaker influence of abiotic variables on forest structure where the intensity of the primary human disturbance factors, forest thinning and cattle grazing, had been strongest.
However, another study from Beerends [28] based on 25-s commercials reported asymmetric interaction effects with a noticeable influence of the video quality level on the perceived audio quality (0.5 on a 5-point MOS scale) and a weaker influence of the audio quality level on the perceived video quality (only 0.15 on a MOS).
Overall, the level of invasion has a weak influence on pollination network structure and seems to be associated with only one metric, H 2 ′ which measures the level of selectiveness; thus, as invasion progresses, species in the network appear to become more selective in their choice of partners, interacting with less abundant species more than would be expected by chance.
As the article notes, gas prices do seem to exert a weak influence on voting behavior.
Servo voltage has a weak influence on average wire amplitude.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com