Before diving in to which stores to visit, make sure you take some measurements. You may be short and fat, but are you equally proportioned? I know I'm not - my torso is normal length, but my legs are not, so stores who sell petite length tops are no use to me, but I do need petite size in skirts and slacks. However, I am 5ft (1.5m) tall and I have to say I have not yet found anywhere where petite size is short enough.
First and foremost I shop for clothes online because websites give you more information about clothes. I have measured myself and know what length of top I like - around 31 inches. I go through catalogues and websites and I'm ruthless - you have to be - if it's not the right length, I ignore it unless it is really fabulous, in which case I look carefully to see if I could shorten it myself.
Whether you can find petite plus size clothes depends on how 'plus size' you are. There are many ranges which will go up to a size 3x, (Lands end, for example, do plus size petite to a size 3x) but beyond that, no. For some reason if you are any larger you are assumed to be an amazon of at least 5' 9". JCPenney, for example, have a plus size petite range, but I could find precious little online above a size 24. Internet searches aren't really useful either, as they often seem hopeful when a brand has a petite range and a plus range, but so often there is no overlap at all.
Lately Ive bought quite a few things from amazon.com, but these were mostly tea shirts from the Daily Ritual brand which I find is great for weekends or under a jacket. I've also bought quite a lot from Torrid. Their listings are very informative and since I know what length I like Ive been able to find some tops in their general range. They don't have many items marked petite but I did find some, though in my case ALL the dresses - and some of them are lovely - were too long, even in the shorter length, but I liked them so I'm taking them up. Some websites will make to your measurements - my most business like clothing at the moment comes from Astartewoman.com, which I can recommend. My underwear mostly comes from Torrid and the rest from all over the place. Old Navy sell slacks and jeans up to size 30 in short, medium and long. I know there are several plus size stores that will sell pants to any length you require, I'll try and update this answer when I find their names, sites like https://www.sumissura.com will create made to measure business suits for both men and women, and of course there is eshakti.com which so far I haven't tried, but I'm looking forward to it since they make to measure. I'm not sure if that's been any help at all, but I am planning to update the article soon, or maybe write another, so if you have found a good experience in plus size petite shopping, please let me know and I can add it to the list.