You have the right to a strong body, and you can have one. Strength improves over time for virtually everyone who trains for strength. You have no need to believe you can't get significantly stronger. Regardless of age, fitness level, genetics, and lifestyle, virtually everyone can significantly benefit -- scratch that, the fact is everyone WILL benefit -- it's that certain -- from strength training. This may be something you've heard before, but keep it in mind: in this way, strength differs from other physical attributes, a lot of which are less changeable. Your body is made with the ability to build muscle and gain strength.
People of all ages can gain strength through training. Training creates good stress. The right level of stress disrupts your system without hurting you; hormones, rest, and your metabolism cause you to adapt to the stress (get stronger). Next time you train, you can lift just a little bit heavier. Virtually everyone can do this. Do the right things, and your body improves (gets stronger). You can't prevent it. Amazing! And it's all yours.
Strength training lasts. Aerobic conditioning decreases fast when you stop (and is also easier to regain). As you get stronger, you'll maintain your strength longer than you assume. For example, after a vacation or other layoff, you won't be starting from zero again. Not even close. You should train methodically a few times a week, but when you miss some training, muscle memory (referred to as "neuromuscular efficiency") helps you come back.
Patience is a virtue. Lots of people, maybe most people, who come to me for strength training doubt their ability to do it safely. It's not because they're not confident people, but because they don't yet know how strength training works. If you've never tried it, you may be carrying a sort of unconscious belief that lifting weights is for strong people. In fact, lifting weights is the best way to get strong when you're not, and that's how those strong people got that way. But your willingness to progress gradually -- even if it comes from nervousness -- pays off, because gradually is the way the body builds muscle and gets strong.
Here are some of my other, brief recent thoughts on weight training. And from my post a while back on my gym web site, here are some of my other thoughts on why you should strength train.
Let me know if you have any questions or want me to back up these statements when we meet!