"Ich habe das Buch auch weiterhin gelesen."
No, there's no hidden negation, that's just wrong. For the redundance, again, it's an emphasise, those two words are often found together. I wouldn't assume they're idiomatic, rather a collocation. [Forgive me, in case I'm using the wrong tense in E.]
Ich habe das Buch gelesen – I've read the book.
Ich habe das Buch weitergelesen – I've read the book on.
Ich habe das Buch auch weiterhin gelesen – I still have been reading that book
'auch weiterhin' can range from 'I'm still busy with that' to 'no, I didn't give up yet' to 'against all odds' you've been doing whatever given, it often carries a defensive tone. Wolltest du das Buch nicht lesen? – Ich lese es auch weiterhin. - Didn't you want to read that book [e. g.: did you already give up?] – I still keep on reading it.
Thank you. I'm a little puzzled by the tense of "Ich habe das Buch auch weiterhin gelesn." It sounds like present perfect (habe gelesen) which would indicate action completed in the past; but "still" doesn't seem to sit right there. Maybe it's only in English that it seems odd, because "I was still reading that book" does make sense. Am I completely off base here?
You might be right, hence my little disclaimer – I don't know if my english was off. Another translation for 'weiterhin' is furthermore which might be more appropriate here. Anyway, the sentence suggests, someone read the book on, somewhere in the past. There's no indication if he finished that book anytime soon or never at all – he only kept reading it a little more, sometime.