I am sponsoring a visit visa for my Cuban partner. He has 2 previous travel visas as history, and we have provided evidence of his ties to Cuba (stable job, leave of absence, immediate family he supports), plus bank statements for both of us, payslips for me, and statements for 2 pre-pay cards in my name to evidence the source of his savings (although I will be paying all the costs of his trip). I typed and signed my sponsor letter - should I have hand-written it? I thought a typed letter would be clearer to read, but we've been waiting 2 weeks for a decision and I am worried they may think a typed letter isn't genuine and refuse on that basis.
Speaking from experience of sponsoring UK visitor visas for family members many times over the last 10 years or so, I can confidently say that typed letter is perfectly fine. Naturally, it should have your signature at the bottom, signed by hand (although on several occasions a scanned/printed copy was accepted, which obviously did not contain the original signature).
Depending on which country you are applying from, 2-3 weeks is absolutely normal. In fact, even a month is not too abnormal. Last time I sponsored a visitor visa for a relative was only a few months ago (January 2017) - and it took about 3 weeks from application to the decision.
Just relax and don't worry about things like this. Provided everything else is in order, the visa should be issued.
UPDATE: It's worth emphasising that the sponsorship letter, just like all the rest of the supporting documentation, must be in English.
The typed letter should not be a problem. I submitted a print of an unsigned email from my sister, inviting me to a 60th birthday and advising she would facilitate transport and accommodation in the UK. Handed in documents 16 May 2017, received couriered passport with visa back on 31 May 2017. Also suffered from extreme post submission anxiety because you prepare all this information and then at "interview" you get no indication if it is acceptable or not. It is just sent on as is to a back room for a decision. Best wishes