I would say “if it is based…” not “given that it is based…” because it is not necessarily the case.
Well if you compare to a portfolio replicating an equal weight index, as not all stocks gain value in the same proportion in a given period, the portfolio is no longer equal weighted at the end of the period, so it is no longer a good replication of your index. You will have to rebalance it.
You don’t have this issue with value or float weighting as, if a stock value is increasing (or market cap) it will take a bigger share of your total portfolio but so does it in your index. So it is still replicating it properly and no need to rebalance