if your lmp was june 1, then you are about 5 weeks pregnant (maybe a bit less if your cycles are normally longer than 28 days).
the website http://www.i-am-pregnant.com/pregnancy/calendar/pregnancy.php lets you enter your lmp and calculates how far along you are.
by "week" pregnancy, do you mean "weak" as in not strong, or "week" as in, how far along are you? if you are concerned that it is weak because of your hcg levels, it is hard to say. the number doesn't matter as much as the rate at which it is increasing. you should have your levels taken again, as they should be doubling approximately every 2-3 days.
as for what you can do, there is not much other than keep taking your prenatal vitamins and take care of yourself. as you can learn by reading the posts on this site, miscarriages are very common, and often occur naturally, not because someone does something right or wrong. when i first got pregnant, even after having healthy hcg levels that were rising, and the doctor seeing the gest. sac, yolksac, and fetal pole, my doctor informed me there was still a 1 in 5 chance of miscarriage. and that was for a perfectly healthy pregnancy (and i am young and in good health as well).
good luck, and it certainly doesn't hurt to say a prayer too.
My lmp was June 1st also. According to that date, with me having a normal 28 day cycle, I'm 5 weeks 2 days as of today. At 5 weeks the normal range is from 18 -7,340. So your within the range even though your numbers are on the lower side. Now you may ovulated late, which may alter your numbers alot.You said that you werent able to carry a pregnancy past 8 weeks. Has the Dr. checked your progesterone levels? That could be a main cause of the uterus not being able to carry out a pregnancy. That should have been one of the first tests performed once you found out you were pregnant. They have supplements of progesterone that can be taken that has helped a lot of women on this forum maintain a pregnancy. Try to get your levels checked again as soon as possible just to make sure there doubling. They can be low, but as long as there doubling things should be ok. I pray things turn out well for you.Good Luck! and keep us posted!