Heavily shorted stocks can become more volatile and move more easily upwards for a variety of reasons.
For one, most of the selling pressure has already occurred, as in there is almost nobody else interested in selling the stock! Existing shareholders don't want to sell, and people don't even want to borrow to sell, and of the people that want to borrow to sell there is nobody else to borrow from!
Short sellers borrow shares from shareholders who do not plan to sell. The short seller then immediately sells those shares to other people, in exchange for cash.
This means there is low liquidity on the sell side, you don't have to buy nearly as much in order to make the share price print higher and stay higher. So just from throwing money at the order books you can make the stock go higher very quickly because liquidity is thin.
Secondly, there are plenty of other ways to do that. Any circumstance that causes pain to short sellers forces the short sellers to BUY BACK their shares, INCREASING the buying pressure into a totally thin group of sell orders, printing higher share prices again. Short sellers borrow money, when they begin owing more money than they started with, they panic and have to close the position by buying back the shares so they can deliver an asset identical to the one they sold and deliver it back to the original shareholder. This is called a short squeeze, and also it happens automatically by the broker if the short seller begins owing too much.
Short squeezes can happen other ways too. Large shareholders can allow people to borrow their shares to short sell, and then disable the ability to borrow their shares ("turn off the borrow") forcing current borrowers to return the shares, but of course the borrowers don't have the shares because they sold the very thing they borrowed!
Hey can I borrow your rare Nike shoes?
immediately sells them on ebay for $1,000 hoping to purchase
identical ones for $400 to give back to you, but keeps the $600
difference in their pocket
If they can't find shares quickly they have to buy shares back at ANY price! These market orders push the price up.