Regards FFC, you refer to four portfolios, which are formed by using different weightings:
The market portfolio, which is a value-weighted return with end-of-previous market cap. as weights:
The excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).
The SMB portfolio, which is the equal-weighted return of value-weighted portfolios, i.e. the six sub-portfolio returns are value-based, and the hedge-portfolio is based on equal-weighted returns of these sub-portfolios:
SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios.
The HML portfolio, which is (as SMB) the equal-weighted return of value-weighted portfolios. Here, the return of four sub-portfolios are value-based, and the final HML return is the equal-weighted difference return of these sub-portfolio returns:
HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios.
The WML (or MOM) portfolio, which is updated each month, and similar the HML is the equal-weighted return of four value-weighted sub-portfolios (see Jegadeesh/Titman (1993)).
MOM is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios.
Carhart (1997). On Persistence in Mutual Fund Performance, The Journal of Finance.
Fama/French (1993), Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics.
French (2019), Data Library.
Jegadeesh/Titman (1993), Returns to buying winners and selling losers: Implications for stock market efficiency, The Journal of Finance.