Does FTL make enemies stronger once you get better weapons?

In the last game, I've got the Ion Beam Weapon (which can disable shields) in the first sector. In this game all enemies in the 2nd sector happened to have 2 levels of shield, thus I lost on 4th due to the inability to break these shields (and no power to use Ion Weapon).

In previous games, I've never seen more than 1 ship with 2 level shields in second or even third sectors. Does it mean that the game adapts the enemies to your ship's setup?

If yes, how can I handle that? Will selling/destroying the weapons which are too powerful for the first sector help?

No, enemy strength doesn't depend on the weapons you have available.

Your situation may have been the result of going into a sector where enemies are more likely to have higher shields (I don't know whether there's a sector type that does this, but sector types do affect what enemies you see), or simple chance (you've only had this happen on one run so far, after all).