From Proverbs 11:3: "The integrity of the upright guides them, but the crookedness of the treacherous destroys them." (English Standard Version)
The answer to the question in the title depends upon how one defines "weak."
Advice and guidance given to Christians in Scripture is based upon the assumption of living under God's rule, living under God's kingdom, and living under God's judgment. If you are not a Christian living under the the rule, kingdom, and judgment of God, you will have a difficult, if not impossible, time understanding why someone would not want, seek, and eventually take vengeance.
Why aren't Christians allowed to take vengeance? Here are the basic reasons:
1. Christians know and understand and accept and cooperate with God's rule over their lives. This means we know God allows injustice into our experiences because He can and will use even those experiences to build and refine us as His children. Please know I am not thinking of allowing ourselves to be misused in abusive relationships. That is never the will of God and someone who acts abusively is not under the authority, or rule, of God, In Scripture, God gives clear guidelines for how people are to treat each other in relationships of family. Nowhere is any reason, permission, or justification given for abuse and mistreatment of others. Abuse breaks covenants. Abuse does not live in covenant relationships.
2. Christians understand what happens when vengeance is sought. When you seek vengeance, you move from God's level and perspective to the level and perspective of sin. Vengeance means you want to do what someone did to you. If they treated you well, you would not seek vengeance. So, vengeance is only sought when someone has been harmed, or sinned against. If you seek vengeance, you want to return the ill treatment. God does not want us to sin in order to heal ourselves or make things right. That process doesn't work, and it recreates more negative energy and anger and ill will in the world. We are here to bless the world, not make it worse or curse it.
3. Christians trust God to handle matters they cannot properly resolve in the natural realm. This is what it means to live under God's judgment, We are not waiting for or expecting punishment. We wait for and expect God to correct those who need correcting. Because He is all powerful and knowing, God will always do a better job of handling our enemies than we could. That is why He says vengeance "is His", or belongs to and is from Him. This is yet another reason why God warns His children to avoid close relationships with people who do not acknowledge and obey God. More angst and conflict and pain is generated from those relationships.
4. Seeking vengeance takes you off track. Perhaps you had a plan, a goal, or a direction. Someone wronged you. You have been deeply hurt or terribly offended. You can get up, plan your recovery, and move forward with your plan. Or, you can spend days, weeks, months, or even years moving away from your goal and chasing vengeance. Now, you are completely removed from your original goal and timetable. Vengeance is hungry, and not easily satisfied. How much of you life do you want to throw away on it? Hopefully, you don't want to throw any part of your life away.
5. Consider all of these things we you think about vengeance and how it makes someone weak or strong. You will probably conclude the strong person doesn't pursue vengeance for the reasons I've stated. It's OK to avoid dangerous, harmful, or angry persons. It's OK to be selective in those you become close with, or spend a lot of time with. It's OK to look at something or someone and decide that thing or person is not for you. However, when you have made your best judgment and someone still harms you, ask God to resolve that matter for you and stay on course with your life. Living well is not the best revenge. The best revenge is not caring about revenge.