Solar differential rotation is an important ingredient of the solar dynamo model, not only because the solar rotation profile is one of the key inputs in a solar dynamo model, but also because it imposes constraints for the solar dynamo model. In this study, we use the sunspot group catalog published by the Coimbra Astronomical Observatory for the period 1929-1941 to analyze solar rotation profiles of different-sized sunspot groups and the dependence of their annual average of the absolute latitude and annual average rotation rate on the solar cycle. The following main results are obtained: (1) smaller sunspot groups (with an area <100 millionths of the solar hemisphere (msh)) rotate faster than larger ones (with an area >500 msh); (2) different-sized sunspot groups drift toward the equator at different velocities of latitudinal drift, reflecting that they are rooted at different anchoring depths; (3) the rotation rate reaches a maximum during the minimum of the solar cycle, which seems to be independent of the size of sunspot groups. The possible mechanisms for the above results are discussed, and we infer that the differences may be due to the different anchoring depths at which flux tubes of different-sized sunspot groups are rooted, their different ages, and the different ways in which sunspot group coordinates are determined.