Why is my player dying when defeating an enemy?

I’m currently making an endless runner based game in c# wherein the player encounters enemies and defeats them by jumping on them. The problem however is when the player jumps on an enemy and kills them, they also get killed in the process. I have a small cube on top of the enemy and it’s set where if the player hits the enemy the player dies, but if they hit the cube then the enemy dies. My code that is being used is as follows:

Player:

void OnTriggerEnter(Collider collider)
{

	if (collider.gameObject.tag == "Enemy")
	{
		DestroyObject(this.gameObject);
	}

	if (collider.gameObject.name == "Weakpoint")
	{
		DestroyObject (gameObject)

Enemy:

void OnTriggerEnter(Collider collider)
{

	if (collider.gameObject.tag == "Player")
	{
		CoinsCollected.coinsCollected++;
		CoinsCollected.coinsCollected++;
		CoinsCollected.coinsCollected++;
		DestroyObject(this.gameObject);
	}
}

If anyone could help me to fix this it would be greatly appreciated!

your code is saying

if (collider.gameObject.tag == "Weakpoint")
     {
         DestroyObject(gameObject);
     }

if I hit a collider with the tag "Weakpoint" Destroy myself (gameObject will refer to the object that the current script is attached to)

if you want to destroy the enemy 
if (collider.gameObject.tag == "Weakpoint")
     {
         DestroyObject(collider.gameObject);
     }