Having to send stickers every time ups the overhead. Also, if stickers are well known variable length files, it may be possible to make good guesses about which stickers are attached.

You could negotiate sticker sending by hash: the first message only contains the hash value, if the recipient already has that sticker stored, it can be displayed immediately. Otherwise the full data can be requested.

EDIT: That scheme can be used to probe whether or not someone already has a specific sticker stored, so it might have to be separated per-contact to avoid leakage.