Researchers in Italy have said obese people may need bigger doses, or another top-up jab, to protect them against the virus.
They claim this is because compared to healthy people severely overweight healthcare workers generated only half the antibodies to fend off Covid-19 after receiving two doses of the Pfizer jab.
Antibodies are virus-fighting proteins that can stop the coronavirus infection.
They are a major part of the immune system but there are other parts too.
This is a double blow to severely overweight people as they are already considered to be more at risk of becoming critically ill or dying if they contract the virus.
Scientists say this could be down to obese people being more likely to have health conditions such as diabetes and high blood pressure which makes them more vulnerable.
Obesity is defined as having a BMI above 30.
Experts said it was also well known that it hampers the effectiveness of jabs as previous research has suggested the flu vaccine could be half as effective in severely overweight people.
But the study by Italian scientists is believed to be the first time the same link has been found for the coronavirus vaccine.
It has been published as a pre-print on medRxiv, and its methodology and findings have yet to be peer-reviewed by fellow scientists.
According to experts, carrying extra weight can lead to the immune system being constantly inflamed which impairs its functions.
In healthy people it only triggers inflammation when the body is fighting an infect
An estimated third of adults in England and nearly 40 per cent in the US are classed as obese.
A total of 248 participants were given two doses of the Pfizer vaccine at Istituti Fisioterapici Ospitalieri in Rome before scientists analysed their blood for levels of antibodies seven days after they had their second dose.
On average those who were a normal weight had a high concentration (325.8) while those who were obese had half this level (167.1).But the study only included 26 obese people - this is too small to make solid conclusions.
More test are needed as there was no significant difference in results between those who were obese and normal weight.
The study also found no significant difference between the different groups.