Upgrading the gun didn't seem to make the enemies die any quicker. On the third level I spawned right next to 3 enemies and died. I like the idea of certain upgrades making you slower, but didn't see any option to not get any upgrade, so either way you get slower on every level.
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That's because there is a useless gun upgrade called bullet speed. I don't know why I made that an upgrade. All of the upgrades are random outside of shops. The levels are random, and in retrospect I should have thought through how I spawn the enemies. I wanted the game to get harder as it progressed, so the weight of things makes you slower after every level regardless to make the enemies more of a threat. The enemy spawn rate is also ticked up for every level you complete.