That all depends on how and why you used the word 'sorry'.
If you had made a mistake and are genuinely remorseful of this and the effects on another, then admitting that mistake is a huge sign of someone taking personal responsibility and as such, is far from being a weakness. It is in fact a huge strength in your character, but...
If you are someone who apologises for everything, saying sorry to appease whether you made a mistake or not or if you aren't really sorry for something but saying it simply because it will make the other person happy, perhaps to appease them by removing their guilt or blame, then it is a huge weakness.
Under these circumstances, it is false, a lie and thats not good. You may get the desired effect from the appeasement, but it will be temporary, and next time, and the time after, youll find it easier to say sorry for something thats not your fault simply for a simpler and more peaceful life. People may then expect you to take responsibility for things that arent your fault, they will treat you with deeper and deeper contempt and your own self esteem will crash. This is a bad situation and an unhealthy relationship and only hurts both parties.
Sorry if youre truly sorry is very good, sorry if youre not or it isnt your fault is extremely bad.
Hope this helps and great question. Thanks :-)