Most of the reports I've seen about COVID and BMI are based on the ICNARC surveys of ICU patients in the UK, the latest of which is here. I've attached the relevant graph to show the BMI distribution of people in intensive care with COVID-19 (blue bars) vs the BMI distribution of people in the general population when you control for age and sex (orange line). You can see that the percentage of people in ICU who are in your BMI category as about the same as the percentage in the general population, so I'm not actually convinced that being obese (as opposed to morbidly obese) significantly increases your risk at all.
There have been a lot of news reports based on this survey saying that 70+ percent of UK ICU patients are overweight or obese, which has been used as evidence that obesity is a risk factor for more severe illness. However, something like 66% of the UK population is overweight or obese anyway, and the proportion increases with age (up to about age 75). So the percentage of ICU patients with a high BMI is likely a reflection of high rates of obesity in the general population, especially the elderly population, rather than due to a higher risk from the virus.
According to the survey the main risk is to people who have a BMI of 40+, who represent 3% of the general population and over 7% of ICU patients, so having a BMI over 40 more than doubles your risk of ending up in ICU compared to healthy weight people. Now obviously BMI is a spectrum and your risk doesn't suddenly halve when you go down from 40 to 39.9, so it's a good idea to try and keep steadily losing weight so that you can be at the lower end of the 30-40 range. But you also don't need to panic!
As EasterBuns quite rightly says, it's hard to say whether the higher rate of serious illness amongst people with BMI 40+ is caused by obesity alone or by the fact that many people in this category will have other underlying illnesses like diabetes and heart conditions (both known risk factors). And as a woman of childbearing age, your risk is extremely low in the first place, so even if you were in the BMI category where it was doubled - which you're not - then that would still make you very low risk overall. About a third of the country is obese, which is about 23 million people, and loads of them will have had the virus by now - even the most conservative estimates of 3-4% of the population would mean nearly a million obese people have had it - and clearly most of them are still alive and well!
By the way, on your point about struggling to exercise, don't worry too much about that - losing weight has a lot more to do with your diet. Exercise is important for your overall health, but it doesn't help that much with weight loss specifically, so you can get your weight down even if you can't do intense exercise. If you can manage to get out for a walk every day then that would be very good for you but it's not the end of the world if you're not feeling well enough.
And last but not least, congratulations on your pregnancy! It's a shame it's happening at such an anxious time, but great that you'll have something lovely to look forward to at the end of all this 
