Big Benz is an odd nickname, and I think while it was probably coined with affection, I feel like it took a bit of a derisive meaning over the years. As Benzema isn't notably big (he's not small, but not big) it might have been more on his lumbering, his often heavy touch when looking forward. Benzema for years had to play either as a striker-in-name-only used to hold up play for Ronaldo, or miscast on the wing. It worked, and often he had success - especially during the height of the counter-attacking Mourinho and Ancelotti years. Benzema was important, but he wasn't Ronaldo, he wasn/t the dominant midfielders of Casemiro, Kroos and Modric. He wasn't even Varane and Ramos. He was just, sadly, a guy - a well compensated, guy.
It's amazing to look back now and see Benzema as the out and out talisman of a still strong Real Madrid when he is easily at best the 7th most important member of the threepeat Madrid UCL team (behind Ronaldo, the three midfielders, Ramos and Varane). While a lot of people will just say Ronaldo overshadowed him, he did struggle with confidence, and more pointedly finishing - especially during his fairly milquetoast 2017-18 season - a large reason why Madrid took a huge step back in the league that year. Of course, Ronaldo would leave that summer, and while things were mostly a mess in 2018-19 as Madrid navigated the ill-fated Lopetegui year, when Zidane returned, the symbiosis with teh French legend just had Benzema go off, and he hasn't stopped.
Real Madrid is not a bad team. It has been overstated how improbable this run to a legitimate chance of a Champions League Final is. Let's remember they're the runaway La Liga winners on points and very much on form. But in the Champions League, where they've been outplayed for large stretches, Benzema has been the very equal of three-peat era Ronaldo.
With Benzema's two goals in the first leg of the Semifinal, a far-harder-than-it-looked half-volley from a cross, and an incredibly ballsy panenka, he now has 9 goals in the knockout stages - with potentially two games left to chase down Ronaldo's 10. And really, Ronaldo from that 2016-17 season is the only time I remember anyone being on this extended of a run.
For a quick run through of Ronaldo's exploits that year, he had two goals in Munich in the 1st leg of th QF, a hat-trick in the 2nd leg, another hat-trick in the 1st leg of the SF against Atleti, and finally a brace in the Final. It was magic. This is close, from his hat trick against PSG, to his next hat trick against Chelsea, to his other goal against Chelsea to wrap things up, to finally these two. He is Madrid right now.
Benzema's story is a story of persaverance. Again, don't want to give him too much credit, he was starting as a lock 1-st team player for Real Madrid the whole time, but he was never loved, consistently overshadowed by bigger, gaudier players (and gaudier fees - e.g. Bale). He had his fans in the Bernabeu, and had a great relationship with each of his famous run of managers - particularly his relationship with Zidane. But to see him take flight, a good 10 years after arriving, is just amazing.
Benzema is just a note perfect player right now. His movement of the ball is great. His holding up of play was always good but hasn't dropped a bit. His quick shot reflexes are incredible - see hte goal that broke PSG's heart. His placement on shots is amazing. He is literally a perfect striker, for a player who's almost claim to fame was just never being too perfect.
Madrid may lose on Wednesday. That is, no matter how much black magic they still seem to have in the Champions League, the more likely outcome right now. If that happens, this Madrid run will recede, other than it continuing a new streak of Semifinal appearances (now at 2, after an 8-year streak from 2011-2018). But if they win..... actually let's not even wonder about that. Let's just bask in Benzema's glory, and the long road it took to get here. Big Benz has earned that nickname bestowed upon him, being massive, being huge, being the talisman of the world's biggest club, at long last.