。
Apparently she was sickly as a child.
Literal
She [topic-は] child [period-の頃] sickly was [it seems-らしい].
らしい ('apparently, it seems, I hear') is the inferential evidential marker — pointing to indirect knowledge: hearsay, deduction, or report-based reasoning. Distinct from そう ('seems based on direct sensory impression') and よう ('seems based on personal judgment'). Here the speaker is reporting something about someone else's past, almost certainly relayed by a third party. 病弱 ('sickly, frail, weak in health') is a slightly literary compound (病 'illness' + 弱 'weak') — heavier than just 弱い. Also note の頃 ('the time of'), a softer alternative to のとき when referring to extended life periods.