"weak impact of" is correct and usable in written English.
You can use it to express a minimal amount of influence, impact, or effect. For example, "The weak impact of the new tax law has been widely reported in the press."
Results demonstrate weak impact of some key instruments.
The findings emphasise the weak impact of the agreement on the most important driving forces for industrial energy consumption.
Because of the weak impact of nanostructures on the strength of fused silica, an artificial square notch with a depth of 4 μm was fabricated in fused silica.
However, empirical evidence that combines individual micro-data with macro-information is less frequent and more ambiguous: Some studies fail to find any influence (Micklewright, Pearson, and Smith 1990), while others find a weak impact of local labour-market conditions on post-secondary participation (Tumino 2013; Meschi, Swaffield, and Vignoles 2011; Rice 1999).
However, considering the weak impact of the infection on the life-expectancy of individuals, this explanation seems rather implausible to us.
Afterwards we relax our assumption about the weak impact of time delays.
Our study suggests that variations in precipitation that occur at a geological time scale (> 106 years) may have a weak impact on the erosion of landscapes and on the delivery of siliciclastic material to large rivers and sedimentary basins.
Intuitively, any individual citation will at most have a very weak impact on the success of a citing paper.
Third, physical health shows a relatively weak impact on the QOL of landless peasants.
These bacteria had a weak impact on the number of shared reactions, while they had a strong effect on the common partial EC number set.
This mode was not taken into account in our modeling because of its weak impact on the resulting spectrum.
