There is no such thing as logic with Discord, remember?
Also, he's twice (two and a half times?) as tall as the Mane Six in his usual biped pose, so that in and of itself means he would be heavier than they are. It just doesn't seem that way because we usually see him floating around in a "screw-the-laws-of-physics" manner.
Twilight is very strong. In season 2 she was carrying TOM on her back (at least 1.5 Tons of weight) and now this. Not to mention that with Cadence's help, she had to haul Discord humongous chariot to the end of Equestria (no idea how far it is). This kind of reminded me of Trixie in her golden bed while Snip and Snails hauled it (both Trixie and Discord didn't use wheels).
But yea, I hope that being alicorn gave her a big of earth pony strength boost, because she sure needed it in this episode.