As a general rule, large caps tend to be less volatile than small and mid caps. In other words, large caps tend to go up less than small/mid caps in a bull market and, conversely, large caps tend to go down less in bear market. This suggests that how one chooses to apportion their portfolio between large, mid, and small caps should depend on the investors time horizon. If you are investing for the long term, then a 33/33/33 apportionment should be more attractive than a large cap heavy portfolio. In fact, on a long term horizon, a larger weighting in the small and mid caps would be well worth considering. In the current market conditions, where shares appear to be fully valued but well supported by low interest rates, I personally would stick with a 33/33/33 apportionment for a long term investment horizon.
The attractions of equal weight investing extend beyond how one apportions between market caps to how one apportions within market caps. For example, the RSP (equal weight S&P500) has outperformed the SPY (market cap weighted S&P500) over 10 years, returning 90% compared with 66% - a significantly higher return. (Both of these statistics are excluding dividends receivable.)