A balloon with mass m is descending down with an acceleration a...

Let the upward force be $F$.

When balloon descending down, then $mg - F = ma$ …(i)

Let the mass removed be $m '$.

When balloon ascending upward, then $F - \left(m - {m}^{'}\right)g = \left(m - m'\right)a$
from (i)
$F - mg + {m}^{'}g = ma - m'a$
$mg - ma - mg + {m}^{'}g = ma - m'a$
${m}^{'}\left(g + a\right) = 2ma$
${m}^{'} = \dfrac{2ma}{g + a}$