Upper bound of the difference between two weighted sum

Question

For $a_i \in \mathbb{R}$ and $X_i, Y_i \in \mathbb{R}^+$,

Is there any upper bound of the difference between two weighted sums, which looks like below?

$ \sum_i a_i X_i - \sum_i a_i Y_i <= |\sum_i X_i - \sum_i Y_i| * const $

the const may be any real number related to $a, X, Y$.

I tried $a_{max}$ but I think that is wrong.

if there is no, how about when $a_i \in \mathbb{R}^+$ ?

Thanks in advance!