Without weights try the following!
Perform pushup variations. Pushups build muscle size and strength in the chest, shoulders and triceps. Start with regular pushups, then transition to pushups with your feet elevated. Keep your hands closer together to work the triceps and shoulder muscles. Widen your hands to work the chest.
Perform pullups to build the back, forearms and biceps muscles. Use full range of motion on this exercise to increase the amount of muscle being recruited. Start with your arms all the way down until they are fully extended, then pull up. When you have mastered the pullup for 10 total repetitions, pause at the top of the bar for three to five seconds. If you cannot perform a pullup, perform negative pullups. You can buy pullup bars that attach to your door frame.
Perform dips. When performing the dips exercise, you must use a dip bar or two chairs. Dips are an effective compound exercise because you lift your entire body weight. When performing dips, use full extension. If you cannot perform a dip, have someone spot you by holding your legs.
Use multiple body-weight squat variations. Squat variations build the quads, glutes and hamstrings. Perform regular squats; once you are able to do 25 consecutive reps, progress to one-legged squats. Ideafit.com states, "The squat is among the most effective lower-body exercises as it incorporates most of the leg muscles working through the kinetic chain."
Do basic back extensions to strengthen your lower back. When you can do 15 consecutive repetitions, advance to the glute-ham raises. For the abdominals, start off performing basic crunches, then progress to twisting crunches. Core work with your own body weight will build muscle in your abs and lower back area.
Google these exercises to see how to do them.
Get the OK from your doctor first.
Body-weight exercises are great for increasing strength. Make sure to target all muscles so you do not get muscle imbalances.
Try out pushups, reverse rows, dips, pull ups, chin ups, handstands, etc.
For abdominals do planks, dead bugs, side planks, crunches, oblique crunches, and supermans.
Squats and lunges will strengthen the gluteus maximus, the quadriceps femoris and the soleus but they don't target the hamstrings. A good one for hamstrings is a Swiss Ball Hamstring Curl. Whenever you work the front of the body, make sure to also work the back of the body. Adductor swiss ball squeezes are great for the adductor muscles, lateral leg extensions are great for the abductors.
Try out a martial art like Muay Thai Kickboxing.
Try Rock Climbing or find a climbing wall at your local recreation center to build great upper body strength.
Instead of weights, use resistance bands instead.
Get into using Gymnastic Rings for an amazing and challenging upper body workout. You can strap them up pretty much anywhere that is strong enough to hold your body weight. I'm personally just getting into using rings and love it, and although I heavy weight lift I am finding it even more challenging!
It is amazing for building strength and the thing about rings is you will always be able to progress into something harder so you could use it to get bigger mass, unlike floor routine body weight movements there is always the possibility to overload your muscles even more, and it's great for core strength too.
I ordered some gymnastic rings for only 60 dollars on amazon and they were here within a few days!
Try out some plyometrics!
Pilates, Yoga. There are many different types of yoga that will all help to increase overal strength
Get a hard labour job on the side and get paid for getting strong. Throw some haybails for a farmer, cut someones firewood - pretty much all hard labour jobs will make you very strong. You won't build a lot of mass like a body builder, but you will get very powerful and strong.
Try stand up paddle boarding this summer for a great workout.
There are lots of things that can help you develop strength. Endurance sports may mostly develop your cardiovascular endurance but they will also help you get stronger too. Endurance athletes aren't weak, but they certainly aren't strongmen. For example, taking up basketball for fun will help you increase some explosive strength.
But if you want my opinion, weight lifting is still probably the best thing for your muscles. You don't have to do it all the time, maybe just once every two weeks IF you are also incorporating some other strength building routine into your fitness routine.
For example, just because I'm getting into using gymnastic rings about 3 times a week doesn't mean I'm going to stop going to the gym entirely. I'll still be going to the gym to lift weights once every 2 weeks, just to make sure I can maintain an overall well-balanced workout along with the hardcore ring training.
Weight training is great because you can target every muscle and know for sure that you are not developing muscle imbalances.
Any sport that uses body weight training is unfortunately bound to give you a muscular balance after awhile (IF you don't know what you are doing and are not working the muscles you are missing on the side) - for example muay thai kickboxing focuses primarily on working the front of the body: there are so many kicks, punches, pushups, jumping squats, burpees but there is never any focus on working the back of the body. If someone doesn't know any better and doesn't spend a lot of time at the gym working the back muscles and hamstrings on the side of all the muay thai training, they will develop a weak back and will become prone to injuries.
A rock climber doesn't use all of their muscles equally either, so they also have to go to the gym and lift weights to incorporate muscles they don't target.
Sports specific training is important to build strength in the muscles the athlete is not using as well as the muscles they use all the time.
You can develop a plan that hits all the muscles with nothing but a floor routine, but in my opinion nothing really beats dumbells because they make it so easy to develop strength anywhere.
But if you still really hate lifting weights, just make sure to work every muscle so that you don't develop muscle imbalances. Here's a list of all the muscles you should be working, then you can simply google search body weight exersices for them for tons of different ideas.
Gastrocnemius and Soleus (calf muscle)
Abductors and Adductors
Deltoids (anterior deltoids, lateral deltoids and posterior deltoids)
Rotator cuff SITS muscles
(Some body weight exercises will target more than one muscle, which is handy)
Pretty sure I covered them all... looking up routines for the muscles might help you come up with further ideas.