Some email services such as gmail put emails into conversations. So if you receive an email reply you will also receive a copy of the original message. So if there's been multiple replies the conversation message can become quite large from the first message to the last. Each message might have its own icon. This might make it confusing to delete individual messages from such a conversation.

I do not normally delete individual messages so from that standpoint I am ignorant as to what occurs. But I presume if another message is sent by either party, again the previous messages are included because it is all part of the original conversation topic or story.

Might this be why you are re-seeing the same messages when the person replies to you?