The Presidents were particularly weak executive officials, being elected by the Delaware General Assembly, having no legislative veto, ineligible for immediate reelection, and whose actions required the approval of an executive Privy Council.

New Hampshire:

On January 5, 1776, New Hampshire became the first American state to adopt a formal constitution. Meshech was a leader in the drafting of this document, which served as the basic instrument of government for the ensuing eight years or until the adoption of a second and more permanent constitution in 1784. Under this constitution, there was no established executive, and the legislature was supreme.

North Carolina

Caswell was president of the provincial congress that wrote the first North Carolina Constitution in 1776. As the congress adjourned, it elected Caswell as acting governor. He took the oath of office on January 16, 1777. Under the new constitution, the state Legislature (“General Assembly”) re-elected him as the first Governor in April 1777. He stepped down in 1780, as the constitution allowed only three consecutive one-year terms.

Virginia

Governors chosen by legislature until 1852

From this sampling, I would surmise weak governors are a product of fledgling state constitutions unsure of creating a strong executive.