Sometimes we are working on particular problem and we feel that we are close to the solution but somehow we can't break through this thin edge which separates us from the goal. So we ask question on MSE. And it happens that some commentator gives us not detailed solution but no more that a hint which makes however passage to the solution possible and shortens us a great deal of work and trials. How can we express our gratitude to this good commentator? It is appropriate to leave in comments some more personal remarks?
You should tell them to convert their comments into an answer (preferably a full answer). Then you can upvote that answer, accept it... Comments are not meant for hints or answers; they're meant for asking clarification or adding information. A question that only receives answers in the comments will stay in the unanswered list, people will have to sift through many comments to find the actual answer, comments can easily and irremediably be deleted, they will be hidden by default if there are many comments and they don't get upvoted much, etc.
If they don't, and you managed to solve the problem yourself, feel free to post an answer yourself using their comment as a basis – you can thank them in the answer. If you want other people to edit that answer more easily, you can post it as "community wiki" (which has the side effect that you won't gain any reputation from it).