Let me say this up front: one weight does not work for all your muscle groups. Your legs are far stronger than your arms. Even the act of pressing something away from your body is stronger than just doing curls or triceps extensions. You might find 5kg (~11 lbs) challenging for those muscles, but you won't even feel the difference with squats. Give yourself enough time with that weight, and it won't even feel like you are doing anything with that either. This is true whether you are a child, a woman, or a man.
To Increase Regularly or Not
There is an over-arching principle in all fitness: Specific Adaptations to Implied Demands (SAID principle). If your demands never change, you will never adapt more than you already have.
Many people function under the false impression that having muscle automatically makes them bulky or unattractive. Usually they are looking at elite bodybuilders that have put decades of dedicated work into looking the way they do and feel like that is not what they want. On the other hand if you look at the average track and field athlete, or even Olympic weightlifters, they don't have the same appearance as the body builders.
In short: don't be afraid of increasing the weights. That helps you get stronger, which in turn improves your muscle to fat proportions. While too much fat makes you not look toned, too little fat can give you that bodybuilder look you are trying to avoid. If you eat and train like an athlete you will have the physique of an athlete. That means you'll have to increase the weight over time.
The Fitness Impact
I'll bring up the SAID principle again. If the imposed demands don't change, you won't have any adaptations. To put it another way, if you keep doing the same thing at the same times, you will never see any change. You won't increase muscle any more, and you won't lose fat any more. You have to change something about what you do to cause other changes.
Potential changes that can all have an effect:
- Change of diet: this affects the amount of fat you carry, and if you supply enough training stimulus how much muscle you can put on.
- Change of intensity (increasing the weight): increases the demands on the muscle, which in turn will make it stronger. That in turn increasing the amount of Calories your body burns in a day.
- Change of volume (more sets/reps): increases the demands and endurance needs of the muscle, which in turn will make it bigger. More volume tells your body you need to keep more energy close to the muscle, and the energy systems take up more room.
- Change of training frequency: increases fatigue which can have the same effect as increasing the volume over the course of a week.
- Change in leverages: this is particularly true with bodyweight only exercise. A pushup is harder when both hands are placed next to each other at or above forehead level. That effectively increases the work your arms are doing.
There's a limit to hours in the day, and attention span while training. Increasing intensity when you are comfortable with the sets and reps you are doing is one way to get more out of your exercise in the same amount of time. It's also a good way to challenge yourself.
You don't have to increase every time you work out. In fact it's fine to keep using the same weight for 6 weeks straight and just add reps week by week. It's a strategy that I use myself. At the end of 6 weeks, you'll be more than comfortable with that weight so it's time to increase.
Recommendation for Home Purchase
Get yourself equipment that can grow with you. Either buy an adjustable dumbbell, or buy a dumbbell handle that you can add weight to. Make sure you know were to buy additional plates. I personally have a fully equipped home gym, with Olympic plates and an Olympic barbell. When I purchased dumbbell handles I opted for handles made for Olympic plates. That ensured I could buy more weight any time I wanted from just about any source.
A pair of dumbbell handles and the plates that go with it may vary in price depending on where you live and how many options are near you. It will still be a lot less expensive than buying a number of fixed dumbbells.