Sigma returning after Mega Man X3, where he was supposedly destroyed by Doppler's anti-virus, can be explained by Berkana reviving him after he somehow escaped Doppler's fortress. X and Zero's surprise at seeing him in X4 is because they expected him to stay dead after thwarting the Erasure plan.
In X3, Sigma tried to possess X to finally defeat him, but Sigma never attempted this again in subsequent games and instead focused on Zero. Doppler's anti-virus did inflict permanent damage, and he was hoping that Berkana's experiments would reveal how to fully restore himself. He was never able to discover this himself, hence why he changed priorities.
The background of the final stages resemble those of the Final Weapon stages, both a Call-Forward and hinting at a connection between the research lab and Repliforce. If the research facility was involved with Repliforce, then it's possible that this was where Iris and Colonel were originally developed. This would explain why Sigma targeted Repliforce: he knew that doubt was already cast upon the army following the Erasure incident, and what Colonel's weaknesses were.
The effect this game's events had on Reploid technology are massive. At this point, energy meters maxed out at 32 units, but moved higher from Mega Man X4 to Mega Man X7. Whatever techniques Berkana used to give herself a permanent power boost, compared to the temporary power-ups the heroes gained, were employed as a universal upgrade for Reploids, explaining the bigger meters and bigger attacks used by bosses. (Though this also leads to Fridge Horror, considering that said methods involved ''consuming other Reploids’ souls... which loops back around to Fridge Brilliance in that other technological advancements could make DNA Souls stronger to begin with, making soul-stealing antics unnecessary.)
Said techniques were likely refined by Sigma into what would become the Copy Chips. It's possible that Sigma's goal in Mega Man X7 was to copy X and Zero's DNA so he could absorb them and heal himself after what happened in Mega Man X3 and Mega Man X6.
