DS9 s2e26 The Jem’Hadar
The cop-out explanation from Memory Alpha:
Only one Vorta was demonstrated using telekinesis: Eris. As the DS9 writing staff put more thought into the Vorta following their initial appearance in “The Jem’Hadar”, telekinesis was discarded and deemed a misstep that the writing team hoped viewers would forget. (Star Trek: Deep Space Nine Companion, p. 155) Ronald D. Moore stated, “Our internal rationale has been that Eris was given this ability for a specific purpose by the Founders (and maybe several other Vorta along with her) and that it is not a normal part of the Vorta ‘recipe’ in the Dominion.” (AOL chat, 1998) However, on an earlier occasion, Moore stated that other Vorta “presumably” had the ability, but no situations in which it would manifest had come up. (AOL chat, 1998)
The Vorta were all genetically engineered anyway, and it would be make sense to customize them for the job they were assigned. I assume that Vorta agents had that power but commanders and politicians didnt. The Founders did go out of their way to ensure all their servants were excellent and their job, but terrible at everything else.
Weyoun saying that his eyes were not so good was probably an intentional decision by the Founders for his position. He didn’t need to see that well, but he did need to strategize (and hear things).