Avariciously tells you HOW someone does a thing: they do it out of that too-strong hunger for money or goods. A person may gather land avariciously, or look at a will avariciously — the action has that greedy-for-wealth colour. The word has the same formal, cold, judging feel as avaricious. Everyday English more often says greedily, though actually greedily is wider (cake, praise, sleep). Avariciously stays close to money and possessions, and it almost always sounds unkind.