The way I interpret Re:Zero scenes is to look at the entire series holistically. Echidna notably cried during Emilia’s 2nd Sanctuary trial in Episode 47, in which Emilia was shown an unthinkable present in which Petelgeuse and Fortuna had frequently gone out together with them going on a picnic with Emilia on that particular occasion. I can’t believe that Echidna had been crying at the sight of Emilia being happy although if she hates Emilia as she claims, it’d make sense since seeing Emilia happy and strong would be infuriating. I don’t know of any woman or man who can hate someone so much that he or she would cry at the sight of her being happy, and so tonight, I’ve formulated an alternative interpretation as I can’t help but believe that something is amiss.
We know based on Petelgeuse apologizing to Flugel-sama before taking in the Sloth Witch Factor meant that Petelgeuse likely promised Flugel not to do so, and that Flugel may have had more Authority in the Witch Cult than Petelgeuse, possibly being a potential founder. Echidna also had Puck enter into a contract with her in which if he entered a contract with Emilia he would lose some of his memories, the tell being when the special font from The Frozen Bond OVA was reused in Season 2 to denote Echidna’s speech, and these two incidents show that both Flugel and Echidna possessed future knowledge and did what they did so that Petelgeuse and Puck would only take in the Sloth Witch Factor and enter a contract with Emilia when there was no other choice, which shows that they were specifically trying to steer the world to a particular future, which we know was 100% true with regards to Echidna for 400 years before the start of the story up until even the end of Season 2 and possibly beyond. Pandora also specifically said that her goal in bringing Regulus to Elior Forest had already been fulfilled, leading to her returning him home with powers, which shows that she specifically brought Regulus to the forest to force Petelgeuse to take in the Sloth Witch Factor, eventually drive him insane by having him kill Fortuna, and have Emilia freeze the whole forest.
So judging by all of this, all of Echidna, Flugel, and Pandora are trying to make a specific future happen, and I’d be surprised if there was no collaboration or knowledge of what the others are doing, which is why I have proposed that they are all on the same side. If that’s the case, perhaps the reason Echidna was crying is that she robbed Emilia of being potentially happy with Petelgeuse and Fortuna. Perhaps, they didn’t have to instigate Emilia losing everything back in the past when that event in Elior Forest happened when Echidna brought Regulus and the Black Serpent with her, and in that sense, Echidna feels guilty for what actually happened, which would be the reason for her tears.
And yes, I know the big thing I have yet to do is suggest why I believe Echidna might actually like or love Satella, and I’ll get to that eventually. We know whereas other Witches of Sin simply call Satella by her name, Echidna calls her Satella, the Witchy of Envy. We know from Seasons 1 and 3 that there is knowledge about the Witches of Win that have been lost to history with Crusch believing Satella created the White Whale when it was Daphne, the Witch of Gluttony, who was revealed to have created the Three Great Mabeasts in Season 2, and that Typhon’s name didn’t become commonplace with how nobody knew the corpse of the witch in Kararagi in Season 3 belonged to Typhon except for Al. This shows perhaps a deliberate intent to conceal or make lost to history information about the dead Witches of Sin, which is an activity Echidna deliberately partakes in as seen by how she said that Satella killed the other witches and used them for sustenance, which some critical thinking debunks since if Satella had done so there would be no corpse of Echidna at the Sanctuary. Thus, I conclude that for whatever reason, Echidna is very invested in making sure that Satella is the bogeyman for all the evils of the world, and this is likely part of her grand plan to ensure that the world, including Subaru, unites to kill Satella at the end of the story.
How does any of this show that Echidna likes or loves Satella? In Episode 49, Echidna spoke in Ryuzu Shima’s voice, saying “Unbelievable. You see this, and that’s the first thing you think of?” after the first thing that comes to Emilia’s mind is getting the original Ryuzu Meyer out of the crystal and taking her to the graveyard. How this is relevant is that Echidna has acted very clinical in how she presents herself to others, so Emilia’s words must have stirred something within her. We know that Echidna can break out of the character she plays as seen by how she said she didn’t want Subaru to think that she was the only one of the witches who was evil, leading to her taking away his qualification for entering the tomb since he was using that as a crutch instead of genuinely helping Emilia. Perhaps the reason Echidna had that thought is despite sounding/being irritated she respects and even admires Emilia’s selflessness and propensity to help others. We know that Echidna hinted that she isn’t even adverse to helping Emilia with how she revealed to Subaru that after three days of trial of error she had no hope of breaking Emilia out of her shell, which shows she tried to help Emilia pass the trial even against Subaru’s wishes since he had been determined to not let Echidna keep making Emilia cry, and that isn’t something you do for someone you actually hate even though Echidna claims that to be the case.
If Satella was a previous heroine of the story much like I have proposed in my main theory, she may have been a lot like Emilia since I expect the heroines to mostly fit the same mold even if they aren’t exactly the same person, and thus, Echidna might have also respected or admired Satella. If my theory about a group of characters from 400 years creating a grand plan to steer the world to a future in which the world is saved, breaking the cycle of the world being destroyed and reconstructed, is true, Satella might have sacrificed all of her life’s potential to help enact this plan by becoming the Witch of Envy, and Echidna might have seriously respected that decision despite the cost it would bring to Satella. If Echidna knows that Emilia is headed towards her life also being sacrificed, maybe that’s the true reason for her tears.