Love can be both a weakness and a strength, with its nature being dependent on the subject of love (given that you referred to romantic love, as there are many types of loves).
Regardless, this weakness and/or strength is only temporary and prone to harm.
When the object or subject of love has major if not optimal control over you, like that of a tyrant, then you can definitely say that love is weakness, as your feelings of affection grandly weakens your resilience and resistance from the one you love, given the loved greater power and influence on you. A perfect example is from the Turkish soap opera “Magnificent Century”, a show that tells the tale of Sultan Suliman I, a great ruler of the Ottoman Empire, where he is highly influenced by his mistress Hurem, until the point he even, for example, executes his closest childhood Ibrahim, a result of rivalry between him and Hurem, where Hurem wins by persuading Suliman with her seductive skill. It is even said often in the show “Behind a great man hides a powerful woman”.
When you make your loved one a source of meaning, a reason to endure life along with the entirety of its hardships, a motive to overcome despair, depression and even suicidal dependencies - then your love is your strength until the intensity of this emotion would fade or be converted to agony, such as the case where your loved one dies or at least abandons you - then your strength is inverted and becomes a great weakness.
Overall I would say that love is a great strength under two terms, that you are assertive enough to not be easily ordered around by your loved one while being able to resist and advocate your opinions, and that the likelihood of your love to that person (like theirs back to you) to endure for the long term - is very probable. Such companionship would be a good engine to motivate you, and a good shield to protect you from the different poisons life is to throw at you.
This is of course, until your love fades or until you give in to your love more than to your individuality - these are two dangers that are very likeable with a lack of sufficient self-monitoring.
I still think self-sufficient love is a better idea, though, as it would be very more likely that your love may die when you die. Do not, however, confuse this with narcissism, as narcissism is delusional self-love, not a mature, conscious and rational one. Not all those who suffice with their love towards themselves think that they are the best person in the world, that they are superior than all beings, and so forth - all of these beliefs are delusional and a compensation for lack of authentic self-confidence. The self-sufficient love I talk about is of another nature - a logical, proportionate and non-compensating one. Thus I coin the term Rational Self-Love, the opposite of narcissism; a love of oneself based on the following logical structure:
1. Love is a good source of motivation.
2. Depending love for others would mean that this good source of motivation may also depend on others.
3. Depending one’s needs on others is counter-productive when the need’s feedback may change uncontrollably, and when one can supply the feedback’s need oneself, especially when considering this self-sufficiency more effective and more enduring (as in this case one can control the need’s feedback when one is self-sufficient).
4. Love is a need that can be self-fulfilled sufficiently even if it can be fulfilled by others.
5. Self-sufficient love is more beneficial than romantic love, where the emotion of love is most intensified.
That way, Rational Self-Love (RSL) is not delusional like narcissism is, as delusions are by definition logically fallacious, and RSL does not have to involve extreme egotism, arrogance, overcompensating protection, or megalomania like narcissism does; RSL brings simply safer, more controllable and therefore more certain, benefit than romantic love, which can be also a weakness once you either lose your assertiveness, or when your loved one departs, or both. RSLers can love others and be altruistic, just not on the romantic level, which may be arguably the deepest level of love, and, therefore, the highest level of risk.
I’ll go even further and conclude that, logically, romantic love ultimately becomes a weakness because the potential of it becoming one is inevitable (the potential losing of assertiveness against the loved one, and the departure of the loved one by various means ranging from breakup to death). In RSL, however, you die with the love and the love dies with you (if you’re determined to maintain RSL, that is, for a lifetime), and there is no risk of losing assertiveness because there isn’t an external force outside of you that may try to order you around while you’re emotionally submitted to it.
In other words, with a sense of love towards yourself that becomes a form of emotional self-sufficiency, the crave for external love becomes less necessary when you're a grown up man or woman. There is also the weakness of external love that should be brought into consideration: the weakness that is submission and the weakness that is dependence on an external source that has a reasonable chance of dying, literarily or metaphorically, leaving an internal void within you.