The weekend theta effect is a phrase used for two different phenomena: 1) It pertains to how options face an extra two full days of time decay over a weekend. And 2) it is the observation of how equities have tended to do better overnight—including on weekends—than when held during the day. This is not always the case but is naturally of interest to active option traders. 

Advanced: The Extra Theta from Weekends

At most of the major brokers, if not at all of them, theta (options time decay) expires based on calendar days remaining, which is displayed as the DTE (days to expiration) remaining at the top of the option chain. This means that there are two extra days of theta to collect from long weekends. Market makers will attempt anti-arbitrage techniques to prevent [risk free] profitable theta collection directly from Friday to Monday, such as allowing implied volatility (IV) to drop as the market moves toward the end of a Friday. 

Expert: Strategy

From a strategic angle, this effect can be used as an edge (competitive trading advantage) if writing and wrapping a spread around each end of an entrance and exit around a weekend. For example, if opening on Wednesday and closing on the next Wednesday, whatever chaos happening around Monday (which might have discouraged arbitrage attempts at the time) would be gone, and the effects of the extra days from the theta collection (cash income over time for taking on the risk and potential obligations of short options) would add up. 

On the other side of this, there is random and potentially severe tail risk if writing (sell to open) naked options over a weekend, especially a long weekend, and this is what long option holders are counting on. There is more time for something extreme to happen with long gaps, and this is what option holders gladly pay for with those extra days of long gamma [accelerated directional] exposure while the market is closed. Also, it is plausible that writing credit spreads over a weekend during negative gamma regimes would be generally harmful to the trader since stronger relative volatility (RV) (the expected percentage range over one year based on historical data at 68.3% confidence) would be expected. 

And on the contrary, collecting theta from credit spreads might generally be safer and more profitable during positive gamma regimes, since there would be more of an expectation for muted RV.