apuntalar

Literally to prop up or shore up a structure (a wall, a mine shaft) with beams or supports, and very commonly used figuratively for bolstering or reinforcing something abstract — an economy, an argument, a relationship.

• Apuntalaron el muro antes de que se derrumbara. — They shored up the wall before it collapsed.
• Esta medida apuntala la economía del país. — This measure bolsters the country's economy.
• Sus declaraciones apuntalaron la confianza de los inversores. — His statements shored up investor confidence.

Using apuntalar for simple physical support of something small (like holding a book upright) — it implies bracing something structurally significant against collapse or failure, so it sounds oddly grand for trivial props; sostener or apoyar fits smaller cases better.