A few things here could use a little clarification. Yes, we are getting heavier, we have for a long time. In fact, improvements in nutrition and diet in general have meant that humans on average are getting taller and heaiver for centuries. It's a comparatively slow and gradual process that is largely unrelated to the concept of obesity. (The growth of humanity, Bogin, B.A. 2001)
That said, we are also getting fatter. There are three primary ways of measuring obesity, as percentage of body fat, as waist circumference ratio or as BMI. (usually the definitions used are BMI >30, Waist/hip circumference > 0,9 for men or 0,85 for women or a body fat percentage exceeding 25% in men and 30% in women. Some countries, primarily in Asia, have lower limits for what is considered obese but lets not get into that for now. No matter how you measure it, we're fatter.
According to the CDC the number of obese americans (measured by BMI > 30) has gone from about 15% in 1960 to almost 30% in 2004. The number of overweight americans (defined as having a BMI 25-29.9) has remained roughly constant at around 30-35% in that time. (Statistics Related to Overweight and Obesity, CDC 2006).
In the same time period the caloric intake of the average american has increased from around 2000 kcal/day in 1970 to over 2500 kcal/day in 2010 ([USDA](https://www.ers.usda.gov/data-products/food-availability-per-capita-data-system/food-availability-per-capita-data-system/#Loss-Adjusted Food Availability) figures). While these figures are not precise they are a good indicator, what research has been done indicates that is anything, these figures tend to be lowballing it with monitored diet figures being upwards of 25% higher than reported.
The rapid rise in obesity in adults began aruond the 1970's and has been picking up pace since then. There is a lot of research as to why we (particularly americans) are getting fatter with people blaming just about everything. A few things are beyond doubt however.
TL;DR - No, the recent obesity epidemic is not merely the continuation of human growth as a result of improved nutrition, medical care and living conditions. We're getting fatter at an alarming rate whereas previously we were just getting bigger at a much less alarming rate.