Blog as both noun and verb is another instance of the process I mentioned a while back, the nounification of verbs or the verbification of nouns (that's not the real name: it's called 'zero derivation' or 'conversion', but that's dull). The process goes both ways, but you get different results. If you turn a verb into a noun, it's an instance of the action: a kick is an instance of kicking. If you turn a noun into a verb, you can't always say what the meaning will be: to fish means to catch a fish, to trouser means to put something into one's trouser pocket and to book means to make a reservation or charge with an offence, and so on. Here I think we've got noun to verb, and I'm fairly certain that this is supported by the date of the earliest appearances of the noun (which derives from weblog) and the verb, though that can be tricky to verify.
Back to blogging a blog and lettering a letter. It's quite unusual that the noun can be an object of the verb derived from it. I can't really think of any examples other than the ones given above, and maybe text as in text message. Maybe message itself. I don't know if it's important that these are all communication acts... you can shout a shout, I suppose, and whisper a whisper.
In US English, the verb is more commonly mail, whereas in British English post is used. But in the US I don't think that mail is used for one particular letter, so you can't mail a mail. When email was invented, the word email was used, probably by analogy with mail, for the general process/system. It quickly became used as the name for a particular message sent by email, as no specific word for this item existed, and for the verb, by the same process of verbification. Thus you could email an email.
You can't letter a letter because there already exists a verb post, or mail if you prefer. We could, when email was invented, have broadened the sense of post or mail to include sending an email, but we didn't, perhaps because it seemed quite different (and in British English, the verb post is not even the same as the one used in email). Post (or mail) likewise would have blocked the use of letter as a verb - but the plausibility of all this is dependent on when each was first used.
So in short, my answer is: because there is already the verb post but there is no equivalent verb for the use of sending an email or writing a blog other than the generic-verb+noun combination like send an email.