I'm not aware of any mention of this in the rules, so this answer is an answer sourced from my judgement.
No, it has no effect on your initiative.
Initiative in combat is a measure of who acts first at the beginning of combat. You roll once in combat for initiative, and then it's done. Your turn order in the middle of combat isn't based on your initiative modifier, it's based on that what happened in that first round.
Being weakened in combat doesn't retroactively affect who got the first shots in five minutes ago. Your initiative isn't affected by being knocked out then regaining consciousness, or being bound up with rope and effectively taken out of the fight altogether, and those are both things which should affect your initiative much more than just being weakened.
Since initiative is something that happened at the beginning of combat, anything which might modify a person's initiative modifier during combat has no affect on their turn order or their initiative. Their initiative has already been had, so there's nothing to modify anymore.