How would blood tests show liver damage from obesity?

AST/ALT. Obesity can contribute to a fatty liver, which in and of itself is not necessarily damaging unless you see elevations of the liver enzymes, AST and ALT particularly. Steatohepatitis as it's called can lead to cirrhosis.
Slight high LFTs. Sometimes obesity can result in a fatty liver, which can be asymptomatic, or have mild liver function test (lft) abnormalities. If alcohol use is involved, there can be progression to cirrhosis, with anemia, prolonged pt, and elevations in alt (aspartate aminotransferase), and ast (alanine aminotransferase), and bilirubin (>10mg/dl).
Slight high LFTs. Sometimes obesity can result in a fatty liver, which can be asymptomatic, or have mild liver function test (lft) abnormalities. If alcohol use is involved, there can be progression to cirrhosis, with anemia, prolonged pt, and elevations in alt (aspartate aminotransferase), and ast (alanine aminotransferase), and bilirubin (>10mg/dl).