Yes thyroid issues cause weight gain.

The problem is this girl in the OP said her adipocytes is storing sugar(glucose) . Here's the thing. It does not and CAN not work that way.

There is NO storage facilitation for glucose, rather it is stored as glycogen (and not in adipose tissue) and that requires processing, and the stores are fairly limited.

Fat people are fat due to a (very usually environmental and changeable) ratio imbalance. That is the ratio of hormone sensitive lipase and lipoprotein lipase in adipocytes.

Here's how it works.

Hormone sensitive lipase(HSL) in adipocytes is the enzyme that transports stored fatty acids from within the adipocytes into the blood (as free fatty acids, FFA). Lipoprotein lipase (LPL) in adipocytes is the enzyme that hydrolyzes the fats and brings them into the cell for storage. This process is very very dynamic. At a stable weight you're keeping on average a balance between the in and out. Gaining weight the average is tipped towards higher LPL content, and losing weight higher HSL content.

This is the only way fat is stored, gained, and lost. It's how it works.

There's multiple things that change the LPL and HSL content. For example Glucagon increases HSL and lowers LPL, while increasing LPL in muscles (so they use the extra FFA now in the blood stream) Insulin does the opposite, reducing muscle LPL allowing it to use the glucose in the blood stream for energy, since more glucose = more insulin to utilize it. It as well increases the LPL in adipose while lowering HSL, since we're not using FFAs in the muscle, because of the abudnance of glucose, it's economic to store the fatty acids, so increasing the inflow and reducing the outflow of lipids in the fat cells is a sensible thing to do.... in the natural world, before cities, before farms... it was sensible.

So that's why sugar being stored in fat cells is silly. Higher glucose and incidentally insulin does result in glycogen storage, but this is mainly in the liver. Glucagon results in the release of glycogen, as insulin and glucagon are inversely correlated, low insulin usually means low glucose, which in turn the release of stored glycogen makes perfect sense as does the use of lipid metabolism for energy (muscle HSL increase) since running full bore on sugar was be a problem since it is obviously now scarce.

Anyhow, /rant.