This is not so much a myth but more of a misunderstood truth. It is entirely possible that you might not lose weight when you start training with weights and in some cases you will gain a little. However, this is a good thing when put into context. Although the scales may not say you are lighter, you will be leaner and smaller - the phrases lighter and leaner are not quite interchangeable. We will pick this up by using our BioSignature Assessment technique and also by taking good old fashioned tape measurements. You will pick this up by how your clothes fit and feel and what you see in the mirror.
What has actually happened is that you will have built a small amount of muscle mass (which is what's happening when you tone up). As muscle is much more dense than fat, it is possible to build 2lb of muscle , lose 2lb of fat, meaning your weight stays the same, but you are leaner and smaller.
My advice ? Let's keep off the scales and use your trousers to measure your progress!