If you can, I would definitely advise investing in a set of weights. I started with 3 and 5 pound weights and now use 6 and 8 pound weights. As I get stronger, I purchase the next size up.
However, you can get away with household items in a pinch, such as soup cans and soda bottles. You could even fill empty milk containers with water to simulate certain weights.
With Physique, the weights are only used in the first 10 minutes for your arms. They've done wonders for tightening and strengthening my arms - but you can skip that part if you want.
The only other supplies you need are a playground ball (which your LO probably has), a chair to simulate a ballet bar and a yoga mat. If you needed to, you could use your LO's foam letter mat with a towel over it.
also - if you don't want to invest in DVD workouts, your cable system's exercise TV channel probably has stuff you could do. There are many many options. You can even look up abs specific workouts online, print them out (or download to your phone) and take to the gym with you.