The phrase "a weak excess" is correct and usable in written English.
It can be used in contexts where you want to describe an amount or degree that is slightly more than what is necessary or expected, but not significantly so.
Example: "The report indicated a weak excess of nutrients in the soil, suggesting that while there was some over-fertilization, it was not at a harmful level."
Alternatives: "a slight surplus" or "a minor excess".
We show that: (a) Some of coronal holes are accompanied by weak excess emission at 17 GHz as compared with the neighboring quiet regions, while the others are not.
Business investment isn't actually all that low; you expect it to be relatively weak in a weak economy with excess capacity, but in fact it's about as high a share of GDP as in the middle Bush years.
Results from our multivariable regression suggest that this policy change had a weak, positive impact on excess mortality in the 65 74 as well as 75+ years age groups.
Although there is a weak signature of an excess of nonsynonymous segregating variation in the D. melanogaster mitochondrial genome, both mitochondrial and nuclear gene sets have median NI, Z*, or NI TG values that deviate in the same manner from the neutral expectation, indicative of both genomes harboring weakly deleterious polymorphisms.
On stratified analysis, a weak positive association with an excess of rs6198 AA (wild-type) homozygotes was seen when the SE negative cases were compared with SE negative controls (Table 2).
Claims in excess of 400,000 indicate a weak job market.
"The department is in a weak negotiating position and commonly pays well in excess of the official valuation.
Another reason that currency movements have little effect on import or export volumes: A weak currency invites competitive devaluations in a world of excess supply.
Thus, we are able to say something about the excess-weight penalty among individuals with a weak connection to the labor market.
In case that both excess temperature and buoyancy flux are unconstrained we assume a weak plume with 500 kg s−1 and 130 °C.
