Here is a list:
- At level 3, your Sorcerer can cast chromatic orb, then chromatic orb. He has dealt 6d8 damage, or 27 on average, to one target. That is the equivalent of one fireball for that target. This is also around the HP of most CR1 monsters.
- At level 3, the same Sorcerer can cast scorching ray, then scorching ray. He has dealt 12d6 damage, averaging 42 damage. Counting that you have 6 chances to crit, this can be far more. You can drop almost any one creature you will face at this level single-handed, if not this round then on the next.
- At level 5, the same Sorcerer can cast fireball, then fireball. He has dealt 16d6 AoE damage, or 56 damage on average. Your tank and glass cannons feel utterly useless.
- At level 5, the same Sorcerer can cast lightning bolt, then lightning bolt. He has dealt 16d6 AoE damage in a line. Same issues as above.
- At level 8, the same Sorcerer can cast blight, then blight. He has dealt 16d8 damage to a single target, averaging 72 damage. Your villain will be really messed up after this one turn.
- At level 10, the same Sorcerer can cast cone of cold, then cone of cold. He has dealt 16d8 damage in a 60 foot cone.
- At level 10, the same Sorcerer can do everything above.
- At level 13, the same Sorcerer can cast disintegrate, then finger of death. He has dealt 136.5 damage (on average) to a single target, assuming they fail both saves.
- The Sorcerer can do any combination of the above at any level where such a combination is possible (eg., fireball and cone of cold, blight and lightning bolt, etc).
I was about to post a related question to this. My suggestion to balance it out is to somehow allow a mechanic whereby, you can spend a number of sorcery points equal to the level of the spell you want to cast. I'm not exactly sure on the balance there, either.
A related but tangential concern is raised by @Alexis Wilke, asking "what's the big deal?" That is, what's the difference between one Wizard casting two fireballs and two Wizards casting one fireball each?
The answer is: a huge difference. If one caster casting two fireball spells is acceptable, then two casters casting one fireball each is suboptimal. Between the two of them, they should cast four fireball spells. You're using a single person's resources in the first case, which is more efficient/powerful than using two people's resources to achieve the same effect.
@Gus raises another good point about the spell slots being limited, which acts as a natural stopper for this. This is true, and it seems to be what is preventing the querent's party mates from spamming all their spells this way.
For small fights, it's no issue; and by "small" I mean fights that the DM meant to be easily winnable. But for boss fights, this becomes problematic. You can bet your players will want to be well-rested before they run into the BBEG's secret lair, and showering them with two high damage spells per caster per round may make that encounter trivial and anti-climactic.