Translation:The disease does not offer a higher risk.
"oferece" should be translated with the verb "present" in this medical context. To use offer here would sound as incongruent as saying something like "The ferocious dog did not offer any hindrance." In English "offer" associates with positive actions. Negative uses of "offer" can be used effectively in comedy: here from Monty Python's Flying Circus; "I'll offer you a poke in the eye." and "I'm offering you a boot in the teeth and a dagger up the strap?"
Yes, I agree. I tried "carry" as well, but it was rejected. "Offer" is simply not correct.
Agreed. I also think "a higher risk" is weird in this context. "Major risk" or "serious risk" are ok.