
Just to underline a key point in this weakness's power, as has already been mentioned. This weakness hits you every single game.
Trying to list every possible way a weakness (even this one) can mess with your game is impossible, but all the basic weaknesses share one, essentially the same, game effect , you loose a round (With the notable exception of Amnesia, Paranoia and Overzealous, all of which can cost you a good deal more). The way Indebted differs? Instead of "When drawn, loose a round" it basically reads "You loose the first round each game".
The first round each game is usually where the team sticks together and drops the assets they mulliganed for on the table, indebted slows this down so you're still setting up on round 2, or entering the fray underprepared, Indebted can wind up on itself, especially if you draw a bad starting hand, imagine the scenario where you get all of your support stuff on the opening hand and no main gear, mystic drawing their holy rosary, blinding light and Arcane studies on the opening hand for example but no Shrivelling or Rite of seeking, playing these cards and paying their costs makes actually playing for your main cards that much harder when you finally draw into them.
How to deal with this weakness? Depending on your investigator you might just ignore it, you might spend your first actions getting back the lost resources, you might start tecking out costly cards. The key positive factor about indebted is that it reduces a lot of pressure and add's a little bit of predictability to your deck. Even so, do not make the mistake of underestimating this weakness. Depending on which Investigator you are playing, Hypochondria and Psychosis are still probably easier to shrug off.
TL:DR. Indebted is the most mitigatable weakness, it is unique however in the fact that it must be mitigated every single game (whereas other weaknessess only show up 2 out of 3 scenarios) and that it always hits you in the very first round.