With each player in a game of Scrabble or Words With Friends getting 7 letters at a time on their rack, 6-letter words can play a huge part in deciding who will win and who will lose a game.
The 6-letter words containing AE on this list are worth 9.1 points on average.
But the best of the lot is worth a grand total of 17 in a game of Scrabble and that word is HYPHAE.
If none of the 172 words on this list meet the criteria that you are looking for then you may find some success with similar lists: 6-letter words starting with AE, 6-letter words ending in AE and words with AE.