A Mughal man of rank comports with a bevy of concubines.
Since I'm a straight woman, that's what I focus on in this post. "Write what you know," and all that, with no slur intended to the gent-loving gents among us. Some or all of the sexual positions for fat men described below would work either way, though, taking into account differences in male and female anatomy.
The Perfumed Garden is an Arabic-language manual of love, written in the early 15th century by Muhammad ibn Muhammad al-Nafzawi, and brought to the English-speaking world in 1886 by Sir Richard F. Burton. In 1999 Jim Colville translated it directly from the original Arabic, thus stripping out many of Burton's fancies and exaggerations. (Unfortunately the Colville edition is rare and hard to get ahold of, so below I use the Burton.) From the Google Books overview:
The Perfumed Garden of Sensual Desire has a tattered history. For over a century, it has been known in English through Sir Richard Burton's bizarre translation (from the French) which consistently elaborated and misrepresented the original. If ever a book needed demystifying, it is this one. Although remarkably lewd at times, it does not linger over details nor does it contrive to excite. It does not, therefore, qualify as pornography. In fact, "The Perfumed Garden of Sensual Desire" is nothing more than a manual for the ordinary, married man of its author's time and place (Tunisia, in the early fifteenth century) -- but one that is not without some entertainment value. This translation is the first English version based upon an established Arabic text, and the first to be translated directly from the original Arabic.
While The Perfumed Garden is full of misinformation, demeaning talk about the "deceits of women," medical errors, and the mistaken notion that two fat people can't easily enjoy sex, I did find interesting this part from Chapter 6:
In the case of the man being obese, with a very pronounced rotundity of stomach, and the woman being thin, the best course to follow is to let the woman take the active part. To this end, the man lies down on his back with his thighs close together, and the woman lowers herself upon his member, astride of him; she rests her hands upon the bed, and he seizes her arms with his hands. If she knows how to move, she can thus, in turn, rise and sink upon his member; if she is not adroit enough for that movement, the man imparts a movement to her buttocks by the play of one of his thighs behind them.
What many like about the "woman on top" is that even if the man has a very large belly, it will "spread out" with gravity, providing a pillow of delight upon which she may rest, or even lie down. Or she can sit up straight, or anywhere in between. The woman can move about "belly-dancer style" as much as she wants, with all the rotations, bumps, and grinds of the hips. Occasionally I've heard about more "traditional" men shying away from the position because it seemed "unmasculine," but to me, "on top" has never implied "dominance." Of course, to others that might even increase their enjoyment, to feel the man in a subordinate position.
Or the woman can climb on top, but can face away from the man rather than towards him, as long as she angles herself so as not to pull his penis uncomfortably in a direction it would rather not go. She can support herself with her hands on his thighs, rather than on his arms or chest, and he can support her back with his hands as well.
For variety, the woman can lie on her side facing away from the man, with her body bent at a 60 to 90 degree angle from the long axis of his body. If she needs to raise her lower body up higher from the plane of the bed so that he can get inside, she can put a few pillows under her hip, or can lie on a whole long body pillow. Then she opens her legs widely enough to rest her top leg on his hip, letting him come in from behind - and the angle leaves room for his belly. The resting of the leg helps particularly if the man has wide hips and heavy thighs. Alternately, he can rest his top leg on her hip. If that's hard to visualize, you can take a look at this explicitly NSFW illustration by Austrian artist Peter Fendi (1794-1842.) Uncomfortable sliding of the leg on top can be avoided by resting it on a pillow. This position works especially well during pregnancy, in particular when the woman is far enough along to find "woman on top" no longer comfortable.
The couple can enjoy entry from the rear, the woman on all fours, where the man comes up from behind and rests his belly on her hips if necessary. Interestingly, Burton's translation limits this approach to couples where both are fat, and speaks of it negatively, although many couples make use of it when it is the man alone who is fat.
Some couples have no trouble with "missionary" even when the man is very fat, but others do. One modification of "missionary" is for the woman to lie on her back on the edge of the bed, with her bottom pushed as close to the edge as possible. She can wrap her legs around his hips, or support them on the edge of the bed, or on two chairs or ottomans, or she can raise them to support them on his arms or shoulders. The man stands in between her legs and leans over, entering her. (If she needs to be raised up higher, again, she can use pillows or a wedge.) The man can lean over her or stand up as much as he comfortably can. If he is very large-bellied, his stomach resting on her vulva can give her as great a pleasure as his thrusting, or more. Fendi again explicitly illustrates where words fail, and even shows a large man. (Click the image here for a larger version with a watermark.)
All ways of sexual coming-together flow from love of variety, flexibility, stamina, and imagination - but most of all from the concern and respect the people involved show one another. Fat sex isn't a series of obstacles to be overcome, but rather a physical way of being to be enjoyed and enthusiastically embraced, a positive source of delight and pleasure.