Older cats are more prone to develop certain medical conditions, like diabetes, hyperthyroidism, liver and kidney issues, and vomiting may be one of the initial symptoms, in addition to weight loss. For this reason, your cat needs to have a geriatric blood panel so your vet can see her levels and if there is an underlying medical cause for her vomiting at this time.
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Also, since she's vomiting in the middle of the night, this may be caused by excess stomach acid produced by an empty stomach. If she's given scheduled feedings, and has no dry food available at night, this may be contributing the problem. If she does have dry food available at all times, she may not be eating often enough or she may have acid reflux. Ask your vet if you can give her a 1/4-1 tablet of Pepcid AC to help control the acid, and hopefully, this will decrease her vomiting. Also, if she's given scheduled feedings, feed her right before your bedtime, so her stomach is not empty for so many hours, until you get up in the morning to feed her again.
If she grooms excessively, yes, this problem could be caused by hairballs, and you can give a hairball remedy daily, like Laxatone or Petromalt, which is available in major pet supply stores. Also, comb/brush her frequently to remove most of the excess fur.
I hope all will be well with your kitty!