Who stated this theory – organ in use will develop and if not used will weaken to turn vestigial

The correct option is Lamarck.

Detailed Explanation:
The concept that organs develop with use and weaken or become vestigial with disuse is a central component of the evolutionary theory proposed by the French biologist Jean-Baptiste Lamarck in the early 19th century. This theory is commonly known as the Theory of Use and Disuse, which is a key part of Lamarckism (or the inheritance of acquired characteristics).

Lamarck proposed that:
1. Use of an Organ: If an organism uses a body part or organ more frequently and intensively to adapt to its environment, that organ will grow, develop, and become stronger over time.
2. Disuse of an Organ: Conversely, if an organism does not use a particular organ, that organ will gradually weaken, degenerate, and may eventually become vestigial (non-functional or reduced in size) over successive generations.

A classic, well-known example used to illustrate Lamarck's theory is the giraffe. Lamarck suggested that the ancestors of modern giraffes had short necks, but by constantly stretching their necks to reach leaves on high branches, their necks became longer. He believed this acquired physical trait was then passed down to their offspring. Although modern genetics has disproven the inheritance of acquired characteristics, Lamarck's work was highly influential as one of the earliest cohesive theories of evolution.