I think it's OK to ask. My T does generally look at and respond to e-mail on weekends (though he charges if it takes more than 15 minutes to read/respond, if I want a long detailed response, but that's the same policy for weekdays, too). He says with e-mail, he can choose when to look at it, so it's not really that intrusive. With texting/phone calls, he limits that to scheduling because that is more disruptive (he uses same cell phone for both work and personal). But, as someone else mentioned, what my T does has no bearing on what yours will be willing to do (I know many T's don't allow any e-mail at all).

What I'd suggest is telling him what you'd want from a response if you e-mail him on the weekend. If you'd be content with, say, a one-line response--confirming that he's read it/that he's there--let him know that. So that it wouldn't take that much of his time. Maybe he could agree to check e-mail once over the weekend (and possibly give a very brief reply), but not more than that. I've found that spelling out exactly what you're looking for can be helpful. And to explain why, like if you're having trouble with connection. Maybe even to agree not to send him long e-mails, but just something he could answer with a few words, like, "You're still there, right?" Just a few thoughts...