I [topic-は] many-weeks [even-も] before [from-から] our puppy [object-を] am-searching [explanatory-んだ].
何週間も前から ('from many weeks ago') — 何週間 + も (emphasizing the length) + 前から. さがしている uses ~ている for an ongoing search. んだ adds explanatory emphasis — the speaker is explaining their situation.