Is it permissible for me to use the money I saved for marriage to pay off a portion of my brother's large debts, in order to alleviate his burden, knowing that this amount will not settle all his debt?

You are not obligated to give your brother money to pay off his debt, and this is not required of you as long as you need the money for marriage and do not have surplus funds beyond your needs. If your brother is in financial difficulty (insolvent), he is not obliged to borrow or beg to pay off his debt, and the creditor must grant him a delay. The balance between helping your brother and saving money for marriage depends on the degree of your need for marriage; if you fear falling into what is forbidden (haram (definition)), then you must hasten to marry. However, if you do not fear that, then there is no harm in providing assistance to your brother. Priority dictates prioritizing marriage, unless delaying the payment of your brother's debt would cause him harm, such as imprisonment, in which case providing assistance to your brother would be preferable.