I'm afraid you simply want too much. Already the first requirements, lightweight x sturdy, are actually opposing, you either need something light, meaning a compromise on sturdiness, or sturdy, all terrain, which means the stroller will be larger, heavier, bulkier. The same for the seat - you want a space for a tall child, however you want the stroller to be the smallest kind there is, to fit the overhead compúacrtment on a plane which means an occasional, minimalistic ultra-compact. And to this, you add a low budget that always means looser, less sturdy strollers with small seats. I'm afraid you will have to compromise a lot, especially with a limited budget and a tall child.
From ultra-compacts, though I warn you, they won't exactly be roomy nor all terrain by any means, I will recommend checking the Recaro Lexa, the Ergobaby Metro+, and the Cybex Eezy S+2 which at least has larger wheels. Also, check a Joolz Aer secondhand.
Then, think about a larger stroller, too. Something like a Valco Snap 4 is light but more spacious for your child to have space to grow in, and your push to be more comfortable. And lastly, rethink what your main priorities are, like 1-2 highest ones (is it budget? space? terrain?), and then all else will have to be a compromise. You would not expect the smallest car there is, like a Smart4Two, to have all-terrain wheels, huge limousine-style seats, and extra space for a table, and all that for very cheap, right? It just cannot be done, engineering-wise.