As little as possible! Sri Lanka is a tropical country and cotton clothes are ideal and, of course, swimwear if you are visiting the beaches. Casual but not provocative dress is acceptable everywhere. You should bring your favorite brand of sun tan lotion as it might not be available in local shops.
Wi-Fi is available at all hotels so bring your essential gadgets to keep in touch. If you wear glasses, pack a Spare pair in case of loss or damage.
Bring enough of your prescription medicines too as the brand might not be stocked by local pharmacies.