It's not a paradox. Loose and tight are distinct concepts from aggressive and passive. Loose/tight refers to how many hands a player plays. Aggressive/passive refers to how he plays them, specifically whether he tends to bet more or call more. A player who folds too much to aggression is called weak. Thus, there are many combinations of styles that you can encounter and will have to adjust to. A player can for instance simultaneously be aggressive and weak. Conversely, there are more dials to tweak when you need to adjust to different playing styles.
Good players are usually aggressive (ie. they tend to bet more than they call) but can be both loose and tight. Passive play (tending to call more than they bet) is usually but not always indicative of a bad player.
Against an overly aggressive player, you should bet less and call more to induce him to keep betting weak hands when you have him beat. This is psychologically difficult to do, because subconsciously you want to 'punish' him by raising when you finally have a strong hand against him. But this will only allow him to escape, as the strength of your hand becomes transparent. Whether or not you should adjust your range is a difficult question to answer. If your opponent is routinely goes too far and bets his weak hands on all streets, I would try to play as many hands as possible against him, because the implied odds more than make up for the many times you will have to fold when your hand doesn't connect.
Against someone who is overly passive, you adjustment should be based on whether they fold too much or too little. Against a passive player who folds too little, play straight-forwardly: Bet when you have a hand, check when you have nothing. In other words, a TAG strategy works best here. Against tight-passive players, play lots of hands and bet all the time (become a LAG).
To summarize: It's not enough to ask if a certain player is tight or loose. You also have to ask whether he is aggressive or passive. The answer to too much aggression is passivity, but the answer to too much passivity is certainly not just more (blind) aggression. Aggression is the answer to weakness (tendency to fold too much) and tightness (playing fewer hands) is usually the answer to looseness. Tight-aggressive play is the style that is the hardest to exploit, but it may not be the one that wins the most money.