Am I permitted to increase the price of an item my relative asked me to purchase, in exchange for its weight and delivery, without informing her of the increase, knowing that informing her might anger her?

It is not permissible for you to purchase an item for your relative at a price higher than its true cost and take the excess for yourself, as this constitutes deception and a breach of trust. An agent may only act within the scope of what their principal has authorized. You are entitled to request transportation fees from her or compensation for the item if the situation necessitates it, or to refrain from purchasing it. However, taking money without her knowledge and consent is not permissible.