This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
She rated herself as the best theoretical engineer at Starfleet Academy, and was fast-tracked in order to serve aboard the Discovery. She initially had quarters of her own due to her "special needs", since she was allergic to polyester and viscoelastic polyurethane foam, which caused her to snore. She then started sharing quarters with Michael Burnham.
Although often socially awkward, Tilly came out of her shell in certain settings, such as the party held on Discovery; even showing aptitude in 20th century beer pong. During the event, Tilly rebuked romantic advances from Lieutenant Rhys. (DIS: "Magic to Make the Sanest Man Go Mad") Paradoxically, Tilly also became a social mentor of sorts to Michael Burnham and facilitated her introduction to future romantic interest, Ash Tyler. (DIS: "Lethe")
According to StarTrek.com, Sylvia Tilly was born with laryngotracheal stenosis. This condition was described as "an abnormal narrowing of the central air passageways that can cause chronic snoring and a dry throat."