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In the set of an index where all insturments are traded in the same time zone I would agree that vola pa from say weekly returns is lower than from daily returns. Besides this, the distribution of weekly returns should look "more" Gaussian than the one of daily returns. This is called aggregational Gaussianity e.g. in the paper by Rogers and Zhang. The term ...

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It is most common to use the "square root of time" method to scale volatility (i.e. standard deviation of returns) to a year (annualize it) if needed, i.e. if the estimate is based on a sample with higher frequency (daily, weekly,..). Mathematically this requires the underlying stochastic process $(X_t)_{t\in T}$ (I've omitted some technical prerequisites ...

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