Candide went through so many things in the book and many of them weren't entirely his fault. It all began with the kiss with cunegonde. This act was innocent in his mind yet he got kicked out of the castle for it. I personally don't feel like it was his fault and that punishment definitely did not fit the crime under the circumstances.
As time went on, however, many of his acts started to become questionable. For example stealing jewel and killing highly esteemed people might not be entirely justifiable at this part in the book. It can be argued that he was solely trying to save himself and cunegonde, but the innocent mindset that he had in the beginning of the book isn't really present anyone.
The way I think of it is that he was a child at the beginning of the book and didn't know any better so he shouldn't have been punished so harshly for kissing cunegonde. But every child at some point reaches adulthood and comes to an understanding of what exactly it is that they are doing. The more experiences candide encounters, the more innocence he loses and the more fault he has in his actions.
Overall, I think that the punishment for any crime in the world he lives in is very extensive. Burning, killing, and beheading criminals is a bit inhumane. Regardless of that fact, if he hadnt been kicked out of the castle, he would've never had to encounter what he experienced and he wouldnt have had to.do the crimes that he commited.