Beta is the correlation or sensitivity of a stock to the overall market. Beta weighting involves normalizing your entire portfolio into reference terms (generally SPY) which largely follows the market. Beta weighting allows the trader to have a better understanding of our overall portfolio risk to moves in the broader market. Normalization is achieved by multiplying key parameters (e.g., the greeks) with the underlying's beta.
At OptionAutomator we use the SPY for U.S. markets as the beta measure. Stocks with high betas (above 1) are highly sensitive to moves in the market and generally move with a greater magnitude than the market as a whole. Stocks with low betas (below 1) are less sensitive to overall market moves. This is seen in well-established stocks, especially those stocks that pay high dividends. Stocks may also have inverse betas (negative betas). These stocks move in the opposite direction to the overall market. A great example of this is the VIX.