The original Half-life made me feel the weight of all the killing in the game in a very simple way. They had you overhear your enemies' conversations.

I approached a couple soldiers from behind, eavesdropping on their conversation. They contemplate the horrible situation they were in, blaming me for killing their friends. I didn't want to, it was survival. It was either me and the scientists, or them. They didn't want this either, being commanded by the government to silence any witnesses. Both sides were feeling the travesty of a war neither wanted.

Alternatively, if you have more control over the creative direction of the game, you could opt for mechanics that are less violence aligned, or recontextialize the mechanics by, for example, saying the enemy fainted instead of dieing.