Central banks have the biggest balance sheets ever, which it means that in order to increase interest rates they will have to sell more bonds than ever, putting additional pressure on the stability of public finance.
Can you explain this bit. If they are getting more interest from the money people borrow from them, why do they need to sell more bonds?
Interest rates in the US and Europe is near 0%. To raise interest rates, central banks need to make money more expensive. To make money more expensive they need to make it more scarce. To make it more scarce the central bank needs to sell the assets in its balance sheet and "sequester" the money of those sales.
The balance sheet of central banks are especially high because we come from a debt-shock crisis which is ultimately deflationary, and because of the Dodd-Frank and Basel III regulations.