。
She's just putting on airs.
Literal
She [topic-は] vanity [object-を] is-stretching only [is-だ] [you-know-よ].
見栄を張っている describes the ongoing display, ~だけ narrows the assertion to 'nothing more than that,' and the final よ delivers it as insider information — the speaker is gently dismissing whatever impression the listener was forming about the woman in question. This kind of ~だけだよ tag is very characteristic of casual reassurance or deflation: 'It's only X, that's all.'