Hi Joy. I did not take a look at your profile before answering your question, so iI am answering this question as if the response is intended for you directly.
One of the primary principles of resistance or strength training is the “overload principle.” Simply stated, this principle states that you make strength gains by performing strength exercises that “overload” your muscles and forces them to adapt by getting stronger. Body weight exercises MAY be used, particularly by beginners, to overload your muscles by performing multiple repetitions and sets of certain body weight exercises. But after some time of training, this method will no longer properly overload your muscles to the extent necessary to continue to gain strength. This is where the use of “external weight” such as free weight and machines comes into play. Since you can progressively increase the amount of weight you use here, you can also continue to make strength gains.
All of this being said, you still don’t need what you call “large fitness equipment” to reach your goal of increased strength. I use many types of weight equipment with my clients, and more often than not, it does not involve large immovable weight equipment. Weighted medicine balls, resistance tubes, dumbbells, weight plates, sandbags and more are all available ways to increase strength without having to use large pieces of weight equipment. If you’re not familiar with how to safely use these instruments, or if you need to determine when you’re ready to progress from body weight to external weight exercises, I highly recommend that you seek the advice of an experienced certified personal trainer or strength coach. And of course as ALWAYS, check with your physician before you begin any exercise to make sure that you’re ready to begin.
I hope this helps.