No, not significantly. If you had a large amount of intramuscular fat and you were losing that fat and building up muscle at the same time, you might increase weight a little for the same size because muscle is more dense than fat. But really, when you increase the "hardness" of a muscle, what you are doing is increasing the amount of fibers than activate upon contraction.
Toning is actually very different. Toning is more about becoming cut with low body fat than the actual strength of level of muscle conditioning.
Some people having started using the term "toning" to mean conditioning of the "tonic" or stabilizer muscles. However, the use of "tonic" is incorrect in this situation as humans have almost no "tonic" muscle. But the misuse is so widespread (I have even seen it in physiology books) it is becoming common usage. The fact that tonic and tone are similar have cause being to conflate the two which is why toning is now often used to describe strengthening of stabilizer muscles.
Open chain exercises will help to increase stabilizer muscles, whereas closed chain do much less more then. This is why I don't recommend machines. Using machines to much can actually cause an imbalance between the working muscles and stabilizers and increase risk of injury.
But I digress...
Right on. I agree with this because there are only three things you can do to a muscle; increase the mass, decrease the mass or increase the amount of fibers activated. Toning has a lot of meanings but I think (and correct me if I'm wrong here) that toning is just another word for cutting. In order for muscles to stand out more, they must either increase in size or have less fat covering them and at the end of the day, these are the only variables that we have control over. (shape, striation depth and pattern, etc. are all genetically determined). So the real question is, are you bulking or cutting (toning)? But to the original question...
Is it possible that as muscle becomes firm (not big) weight will increase?
Not really. If someone is very fat then maybe the intramuscular fat stores would shrink when they lose weight. Other than that, your muscles actually get lighter compared to their strength, since training does increase the amount of muscle fibers at command over time. Muscle density is genetically determined.
Also, muscle does get bigger as it becomes more firm! Muscles get firm when they are full of glycogen (sugar water) but they are also getting larger... I believe you are asking about muscle density. If you want more dense muscle, dehydrate yourself. Think of the way a dry sponge expands with water, the water is like the glycogen. If you take the water out, the muscle shrinks, and is therefore more dense. Also less healthy since muscles are over 70% water...