7. 10 .

By symmetry, without loss of generality, assume $a_{i}<a_{j}$. Then there must exist an isosceles triangle with $a_{j}$ as the waist and $a_{i}$ as the base, and there is only one isosceles triangle with $a_{i}$ and $a_{j}$ as side lengths.
Thus, $a_{i}+a_{i} \leqslant a_{j} \Rightarrow a_{j} \geqslant 2 a_{i}$.
This indicates that, when the elements of set $B$ are arranged in ascending order, each subsequent element is at least twice the previous one.
Therefore, when the number of elements is maximized, the set
$$B=\{2,4,8,16,32,64,128,256,512,1024\} \text {. }$$