Your picture seems to show 2x4s, a doubled sill plate, a gap, then a header. If that header spans from an exterior wall to an exterior wall, the 2x4s and doubled sill plate aren't doing any work other than holding up drywall.

Whoa what happened here loll what a vibrant and fascinating discussion haha. I have learned so much! Here is today's update: Structural engineer said the existing beam is sagging 0.5 inches assuming the floor is level (seems like a terrible thing for a structural engineer to just assume) and that it's not adequate to support the weight of the upper floor. He said it's not overly concerning but that he wouldn't recommend putting heavy safes or furniture in the master bedroom closet above it because that wouldn't help anything. He said he noticed a bit of sag in the upper floor above where that beam is. About the sloping floor on the first floor (where the inspector observed it): the engineer didn't mention it after he was done inside, and I asked about it when we were outside before he went into the crawl space...after he came out and said the foundation looked good with only minor expected cracks and that any floor sloping wasn't related to the beam issue. Overall, he didn't think the structure of the house had been negatively impacted enough for us to be worried about buying it. He said a lot of old houses have slightly sloping floors and since this house was built in the 90s, it wasn't old enough for him to be too worried about it. He did say we could do a partial wall if we wanted to avoid doing a beam, so I asked him to include the calculation for how long that would need to be to be adequately supportive and he said he would, just in case we want that number later (and to make him do a bit more work to make myself feel better about getting my money's worth hah jk I really would like to know). He said it would be a range because he would have to make some assumptions about the internal joists/framing. I also walked around with my humble little level and checked floors and doorways and window sills and everything looked good to me. Interestingly, the owners thought only the engineer was going to be there today, so they were surprised to see us arrive with our realtor and two kids (awkward) but apparently....sometime after they bought the house, they added the original walls back in to have an extra bedroom, and then when their kid(s?) moved out, they took them back down again. Not sure exactly how that was executed or how on earth (pun intended) they didn't leave any indication of that on the wood floor but seems like they might have failed to disclose something they should have. But that explains so much... It gets better. The two hooks you see on the left side of the inadequate beam: they were used for a child's swing 😂👍 The owner cheerfully volunteered that information to us all. Maybe she was trying to prove that the beam is fine haha? Sigh. I'm still trying to process everything. I'm annoyed at myself for not thinking to ask the owners what duration the wall had been in place and if it was an actual wall that supported the ceiling weight....bc if a real wall had been there for, say, 14 of the 16 years, then the whole "if it's been fine for 16 years, then it's probably going to be fine" type of logic might be in question. But then I could at least know that the house frame wasn't strained for ALL those years. Anyway, guess it doesn't matter too much now.. At least now, a hefty $1100 later: I know that the current beam is inadequate. But the house structure and foundation don't show signs of concern (except for the slight sag upstairs - still not sure what to make of that...maybe the report will clarify...but if we put in a new beam asap, then hopefully it's considered fully remedied and not a disclosure that will negatively impact the value of the house). I'll have a written report to share with contractors or potential future buyers if this issue comes up when we move and need to sell down the road (assuming this deal survives and we actually get the house...). Or maybe I'll never look at it again.. Also thinking about whether this info can work into our current negotiations so perhaps the report will pay for itself and some of the beam. I have some peace of mind about moving forward. I know a bit better what to expect, and a bit of documentation (hopefully soon) in case I ever want to prove something to someone. Still would have loved to hear that the existing beam was legit but that would have been too easy. Thank you all so much for your investment in my situation. I am truly humbled (and entertained) by your incredible wisdom and experience and super grateful for all the input I have received here!!!!!

A nook for a stove won't work very well. You need a minimum amount of clearance on both sides for the stove to be functional. And in fact, many manufacturers have minimum clearance requirements to meet fire code. This is usually on the order of about 12" on each side, although in practice that's really tight and awkward. I'd recommend at least 18" and preferably 24". Your drawing makes it look as if you won't have sufficient space to do that. So, you probably wouldn't be able to get the work permitted -- and even if you did it without a permit (which I won't recommend), you'll suffer from a poorly functional layout. The overall layout of the kitchen looks pretty awkward to begin with. I love cooking and like a very functional kitchen, so I probably wouldn't bid on the property because of that. Your situation might be different, depending on how important a good kitchen is to you. Having said all that, cost depends on so many different factors. It's really hard to say. It could be as easy as installing a new header, repairing a little bit of sheetrock, and patching the floor. Depending on what materials you choose and how expensive your local labor market is, I could see an absolute low-end price of around $2000 if hiring a handy man (not a great option when doing structural work!). But in a HCOL part of the country, with higher-end materials, and maybe a complication or two, it wouldn't be unusual to cost $20,000. And if you have to involve a structural engineer, an architect, and a few iterations with the planning department, you could even double that cost. If the city makes you bring things up to code in the process, things could balloon even more. The good news is that while all kitchen remodels are expensive, once you get to the upper end of the price range, there only is a small incremental difference between moving a wall and doing a full remodel. So, the good news is that at least you'll get a lot more for your money; the bad news is that until you actually get quotes and maybe have somebody open up walls, it's really hard to give you any firm numbers.

You need to have someone that knows about load bearing walls (not just someone off the street), to come in and do a thorough inspection. They will need attic access, to do this. As to those two 2x4 you want to remove, well, you can be assured, they were not just put there, because someone wanted to put in some 2x4. They are there for a very good reason. Its just the way the house was built., so dont remove anything more until you get it inspected.