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Let p be a rational prime. Let F be a totally real number field such that F is unramified over p and the residue degree of any prime ideal of F dividing p is 
$\leq 2$. In this paper, we show that the eigenvariety for 
$\mathrm {Res}_{F/\mathbb {Q}}(\mathit {GL}_{2})$, constructed by Andreatta, Iovita, and Pilloni, is proper at integral weights for 
$p\geq 3$. We also prove a weaker result for 
$p=2$.
