Final answer:
The formal powers of a weak mayor in Texas are most similar to those of a city manager, as both hold limited authority and focus on administrative duties within the government.
Step-by-step explanation:
The weak mayor's formal powers in Texas most closely resemble those of the city manager. In a weak mayor system, the mayor has limited authority and often plays a ceremonial role, not dissimilar to the role of a city manager in a council-manager system of government. The city manager is appointed by the city council to carry out administrative functions, while the mayor under a weak mayor system has limited powers to veto actions of the council, appoint and dismiss department heads, or produce a budget. This setup contrasts with a strong mayor system where the mayor wields greater executive powers.