The characters combine literally and logically: 体 (body) + 弱 (weak) + 多 (many) + 病 (illnesses). The meaning is transparent: someone whose body is weak and thus suffers from many illnesses.
In Chinese culture, health is often viewed not just as the absence of disease, but as a state of robust vitality and balance (often related to the concept of 气 (qì), or vital energy). 体弱多病 represents a significant deviation from this ideal state. It implies an inherent imbalance or deficiency in one's constitution.
This chengyu is common in both spoken and written Chinese and is used in a variety of situations.
The connotation is generally one of sympathy. It's not an insult, but a statement of a person's unfortunate physical condition.