In quantum physics, the concept you're referring to is known as the observer effect or the measurement problem. It states that the act of observing or measuring a quantum system can affect the system itself. This effect arises due to the wave-particle duality of quantum objects, where particles can exist in multiple states or locations simultaneously until measured, at which point their state "collapses" into a specific outcome.
Regarding your first question, the effect of the initial observation does not maintain control or influence over subsequent observations. Each observation is considered independent and can potentially lead to a different outcome. This is because the act of measurement disrupts the quantum system and forces it into a specific state, eliminating the superposition of multiple possibilities.
As for multiple observations of the same object, there is no concept of an "average" change resulting from those observations. Each observation is treated as a separate event, and the outcome of each measurement is probabilistic. The probabilities of different outcomes are determined by the quantum state of the system before the observation. Subsequent observations are not influenced by previous measurements unless the system is prepared in a specific state again.
It's important to note that the observer effect is specific to the quantum realm and generally not noticeable in everyday macroscopic objects. Quantum phenomena become significant at the microscopic scale, such as atoms, electrons, and photons. In the macroscopic world, the probabilistic nature of quantum physics averages out, leading to the classical behavior we are familiar with.