There is no specific equation or exact methodology to picking the right weight for strength training. Your physical size, current fitness level, fitness experience and overall health each play a part in choosing what is the right weight. I use these 5 guidelines when selecting weights for myself and clients.
Form first. This isn't a guideline, this is a must. It is essential that you maintain proper posture and form for each and every repetition. If you can't, the weight is too heavy.
No momentum or swinging is required. With the exception of power moves and some kettlebell moves, you need to be able to do the repetitions without swinging the weights or your body to complete the move.
The last few repetitions of an individual exercise should be hard. You should be asking yourself "are we there yet?" Strength training works by forcing the muscle to adapt and then grow or change. If you don't push the muscle it won't change.
If you breeze through the repetitions or could do more at the end of the set, your weights are too light.
Don't choose your weight based on what someone else lifts. Listen to your body, it's the expert here.
If you like the gym for working out, you have the benefit of trying out a lot of weights. I don't. I established my adult baseline of fitness and maintained it for nearly 15 years with a set of 3, 5 and 10 pound dumbbells. When my goals shifted from "how I look" to "how I feel" I invested in heavier weights because I wanted to be stronger. Building strength requires greater muscle adaptations. I need to lift heavier. Today my dumbbell rack holds those original weights plus 8, 12, 15, 20 and 25 pound dumbbells.
If you are able and want to buy yourself weights, go to the store, pick them up and try a few exercises to see how they feel. (I know, it feels funny but just go for it).
Pay attention to the grip. Is it comfortable in your hand? Handles with foam can be a life saver if you have grip challenges and the diameter of the handle really matters for comfort.
For women, I often recommend 3 sizes of weights.
Light (3-8 pounds) for upper body, especially the shoulders.
Heavy (10-15 or more) for lower body, you want to be comfortable holding these at your side.
Medium (5-12) for your back and chest, but also a mid-range to provide challenge as your strength improves.
If now is not the time for a new investment but you still want to challenge yourself, see my February post on Practical Progressions.