One parameter is 16 bits == 2 bytes. So a model with 7 billion parameters needs 14GB of RAM for the un-quantized model, plus some overhead for the KV cache and other "working memory" stuff but that should be fairly low for a 7B model. I expect it will work on a 16GB GPU just fine.
Quantized ones are also easy. 8 bits == 1 byte so that's 7GB for the model. 4-bit gets you below 4GB.