When to answer and when not to answer a brief e-mail from a busy academic?

I frequently receive brief, usually confirmatory e-mails (such as "Can do. Best" in response to a request for a letter of recommendation) from academics with considerably less time than myself.

Each time this happens, I am very indecisive about whether the nuisance caused by responding -- and adding an e-mail with essentially no information, such as "Many thanks; this means a lot to me! All the best" to their inbox -- really weighs more heavily than the risk of being perceived as ungrateful.

Any thoughts, ideally from the referee's perspective are greatly appreciated!