The phrase "a varying severity" is correct and usable in written English.
It can be used to describe something that has different levels of seriousness or intensity.
Example: "The symptoms of the illness can present with a varying severity, ranging from mild discomfort to severe pain."
Alternatives: "a range of severity" or "different degrees of severity".
Care for the Wild International estimates that at the Tiger Temple in Kanchanaburi, Thailand, a popular tourist destination for Brits, Australians and New Zealanders, there are up to 60 incidents a year (of varying severity) of captive tigers mauling tourists or volunteers.
In almost all infected animals a meningoencephalitis of varying severity was detected.
The data suggest that 127 patients (89%) had noticed a change of varying severity in their bowel habit.
Osteogenesis Imperfecta (OI) is a disease with varying severity affecting physical, social and emotional well-being of the child and their family.
Methods: To evaluate this risk, we coupled a global spatially structured epidemic model that simulates the quantities of antivirals and antibiotics used during an influenza pandemic of varying severity and a water quality model applied to the Thames catchment to determine predicted environmental concentrations.
Also, as Heffer points out, the Pru "is far more likely to pay out for a range a critical illnesses of varying severity" as it has the biggest list of 166 conditions.
We also asked questions about how likely they would be to report a stranger, an acquaintance, a friend and a family member for crimes of varying severity (from petty theft to murder).
Researchers who have completed studies on gambling estimate that 4 to 8percentt of adolescents have a gambling problem of varying severity.
Type 2 diabetes is a somatic disease of varying severity.
The validation study showed that 92.3% mothers who scored above this threshold were likely to be suffering from a depressive illness of varying severity.
